Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 983090983088983089983091 Article ID 983097983094983091983093983091983088 983089983091 pageshttpdxdoiorg983089983088983089983089983093983093983090983088983089983091983097983094983091983093983091983088
Research ArticleRecentering Shape Memory Alloy Passive Damper forStructural Vibration Control
Hui Qian1 Hongnan Li2 Gangbing Song23 and Wei Guo4
983089 School of Civil Engineering Zhengzhou University Zhengzhou 983092983093983088983088983088 China983090 Faculty of Infrastructure Engineering Dalian University of echnology Dalian 983089983089983094983088983090983092 China983091 Department of Mechanical Engineering University of Houston Houston X 983095983095983090983088983092 USA983092 School of Civil Engineering Central South University Changsha 983092983089983088983088983095983093 China
Correspondence should be addressed to Hui Qian qianhuizzueducn
Received 983089983090 July 983090983088983089983091 Accepted 983097 September 983090983088983089983091
Academic Editor Gang Li
Copyright copy 983090983088983089983091 Hui Qian et al Tis is an openaccess article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Tis paper presents a preliminary study on the evaluation o an innovative energy dissipation system with shape memory alloys(SMAs) or structural seismic protection A recentering shape memory alloy damper (RSMAD) in which superelastic nitinol wiresare utilized as energy dissipation components is proposed Improved constitutive equations based on Graesser and Cozzarellimodel are proposed or superelastic nitinol wires used in the damper Cyclic tensile-compressive tests on the damper with variousprestrain under different loading requencies and displacement amplitudes were conducted Te results show that the hysteretic
behaviors o the damper can be modi1047297ed to best 1047297t the needs or passive structural control applications by adjusting the pretensiono the nitinol wires and the damper perormance is not sensitive to requencies greater than 983088983093 Hz o assess the effectivenesso the dampers or structural seismic protection nonlinear time history analysis on a ten-story steel rame with and without thedampers subjected to representative earthquake ground motions was perormed Te simulation results indicate that superelasticSMA dampers are effective in mitigating the structural response o building structures subjected to strong earthquakes
1 Introduction
Conventional structures rely on their adequate stiffnessstrength and ductility to survive earthquakes Such a designstrategy may not be economical and may be ineffective orunexpected seismic events [983089 983090] In recent years the design
strategy based on the perormance o civil structures hasattached increasing attentions o both practicing engineersand structure owners [983091ndash983093] o enhance the seismic peror-mance o structural systems many possible strategies havebeen proposed [983094 983095] and one promising amily o solutionsis the passive control techniques [983096 983097]
By and large current passive control applications arebased on the ollowing two techniques seismic base isola-tion and energy dissipation [983089983088] Seismic isolation systemrelies on special ductile alternate layers which are installedbetween substructure and superstructure to reduce the trans-er o seismic energy to the superstructure thus protectingthe superstructurersquos integrity [983089983089] Usually in order to limit
the extent o the displacement energy dissipation devicesare incorporated into the alternate layers Energy dissipa-tion system incorporates special energy dissipation devicesinto the structures to absorb or consume a portion o theseismic energy thereby reducing energy dissipation demandon primary structural members and minimizing possible
structural damage [983096] Nowadays several types o seismicenergy dissipation devices such as metallic dampers rictiondampers viscoelastic dampers and viscous 1047298uid damperare available However current technologies present somelimitations such as problems related to aging and durabilitymaintenance reliability in the long run substitution aferstrong events and variable temperature-dependent peror-mances among others [983089983090] Recently the increasing researchand development o smart materials and controlling devicesopen up a new area or seismic vibration control o structuralengineering providing a basic platorm or the design andexploration o new generation high-perormance dampingdevices
F983145983143983157983154983141 983089 Stress-strain diagrams o Nii shape memory alloy (a) SME lt 1038389 (b) superelasticity 1103925 lt lt 10383891038389
0
100
200
300
400
500
600
700
800
Experimental data
Te improved Graesser and Cozzarelli
000 001 002 003 004 005 006 007 008 009
S t r e s s 1038389
( M P a
)
Strain
F983145983143983157983154983141 983090 Stress-strain curves o superelastic nitinol wires
Shape memory alloys [983089983091] are a class o novel unctionalmaterials that possess unique properties including shape
memory effect (SME) superelasticity effect (SE) extraor-dinary atigue resistance high corrosion resistance highdampingcharacteristics and temperature-dependent Youngrsquosmodulus At a low temperature SMAs exhibit the SMEmdashresidual deormations can be recovered by heating the mate-rial above the austenite 1047297nish temperature as shown inFigure 983089(a) At a higher temperature SMAs exhibit the SEas shown in Figure 983089(b) In the superelastic phase SMAs areinitially austenitic However upon loading stress-inducedmartensite is ormed Upon unloading the martensite revertsto austenite at a lower stress level resulting in the hystereticbehavior Tese properties make them ideal candidates orseismic energy dissipation devices in structural engineering
A signi1047297cant number o research studies have beenconducted in an effort to use SMAs orapplications in seismicresistant design and structural retro1047297t in the past decade(eg [983089983092ndash983090983092]) Wilde et al [983089983092] proposed a smart isolationsystem combining a laminated rubber bearing with a devicemade o SMA or highway bridges Teir analytical resultsshow that the isolation system can limit displacement anddissipate energy or earthquake mitigation Dolce et al [983089983093]developed two amilies o SMA-based energy dissipating andrecentering braces or seismic vibration control o buildingsand bridges as outcomes o the MANSIDE project (Memory
Alloys or New Seismic Isolation and Energy DissipationDevices) o assess the effectiveness o SMA braces toreduce the seismic response o reinorced concrete (RC)ramed structures shaking table tests o a 983089983091983091-scale three-story two-bay RC plane rame which was designed orlow seismicity and low ductility according to the Europeanseismic code were carried out by Dolce et al [983089983094] Teirexperimental results show that the SMA braces can enhanceseismic perormances at least comparable to those providedby steel braces while having an additional sel-centeringeature Indirli et al [983089983095] retro1047297tted historic buildings usingsuperelastic SMA tie bars to enhance its seismic resistancecapacities DesRoches and Delemont [983089983096] and Andrawes
and Desroches [983089983097] evaluated the efficacy o superelasticnitinol bars as restrainers to reduce the risk o collapserom unseating o bridge superstructures at the hinges Tey ound that the SMA bars are effective in limiting relativehinge displacements in typical multiple rame bridges Liet al [983090983088] investigated the vibration mitigation o a stay cable provided with one superelastic SMA damper Teanalytical results show that the SMA damper can reducecable vibration signi1047297cantly and the control effectivenessis in1047298uenced by SMA damper parameters and locationsZhang and Zhu [983090983089] developed reusable hysteretic damper(RHD) based on superelastic nitinol stranded wires andtheir numerical analysis indicated the effectiveness o RHD
F983145983143983157983154983141 983091 Diagram o RSMAD
F983145983143983157983154983141 983092 Photograph o experimental setup
in passive seismic response control o structures Ocel et al[983090983090]and McCormick et al [983090983091] investigated beam-columnconnections using SMA bars Teir studies show that SMAcan enhance the seismic perormance o the connectionsParulekaret al[983090983092] proposed a damper deviceusing austeniteNii wires Te device is tested and validated using a thermo-mechanical model o SMA taking into account the residualmartensite accumulation Perormance o the structure withSMA dampers is compared with that o the same structurewith yielding dampers
Previous works show that SMAs are o promise in struc-tural engineering particularly as energy dissipation compo-nents or seismic protection However signi1047297cant research
is still needed In Particular designing new types o SMA-based passive seismic devices which possess not only energy dissipation and recentering capabilities but also simple con-1047297guration or easy installation in the practical engineering isstill a challenge
Tis paper presents an innovative recentering shapememory alloy damper (RSMAD) or seismic structural pro-tection Te damper is simple in design and easy to imple-ment Superelastic nitinol wires were utilized in the damperas kernel energy dissipating components Cyclic tensile-compressive tests on the damper model with various prestrainunder different loading requencies and displacements wereconducted o assess the effectiveness o the damper or
structural seismic protection nonlinear time history analyseson a ten-story steel rame subjected to representative earth-quake ground motions with and without the dampers wereperormed
2 Constitutive Equation of Superelastic SMA Wire
With the wide applications o SMAs in different 1047297elds mod-eling o the peculiar mechanical behavior o SMAs such asSME and superelasticity has been an active area o researchover the past decades So ar many constitutive models orSMA have been developed [983090983093ndash983091983091] Tese models describethe thermomechanical thermoelectrical and thermochem-ical behaviors o SMAs however most o them are too com-plex to be convenient or practical application in earthquakeengineering In this paper a relatively simple model devel-oped by Graesser and Cozzarelli [983091983092] is adopted Tis model
is an extension o a one-dimensional strain rate independentmodel or hysteretic behavior proposed by Ozdemir [983091983093]Teequation is given as
907317 = 852059 minus | | 1048616907317 minus 10486171103925852061 (983089)
where 907317 and are the one-dimensional stress and the one-dimensional strain respectively is the initial elastic modu-lus is the yield stress is a constant assumed any positiveodd real value controlling the sharpnesso transition rom theelastic state to the phase transormation and denote thetime derivative o the stress and strain respectively and isthe one-dimensional back stress given by
= in + 907317|| er () [ (minus )]983165 (983090)
where 907317 and are material constants controlling the typeand size o the hysteresis the amount o elastic recovery dur-ing unloading and the slope o the unloading stress plateaurespectively When 907317 = 0 the model is purely martensiticWhen 907317 gt 0 the model predicts the superelastic behavior is a constant controlling the slope o the 907317 minus curve in theinelastic range given by
F983145983143983157983154983141 983093 Hysteresis loops o the RSMAD at different prestrains and displacement amplitudes (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
in is the inelastic strain given by
in = minus 907317 (983092)
() is the unit step unction de1047297ned as
() = 983163+1 ge 00 lt 0 (983093)
er () is the error unction de1047297ned by
er () = 2radic int
0minus2 (983094)
Te original Graesser and Cozzarelli model has a rel-atively simple expression with the parameters that can beeasily acquired however this model excludes the martensitichardening characteristics o SMAs under large amplitudeswhich are critical or structural saety protection underextreme events
o overcome the limitation o the original model Wildeet al [983089983092] extended the Graesser and Cozzarelli model by dividing the ull loop into our parts adding two termswith six parameters into (983089) Te Wilde model was utilizedto simulate the cyclic behaviors o SMA devices in otherresearches [983090983089]
In the ollowing in order to accurately predict the cyclic
behavior o a superelastic SMA device especially capture themartensitic hardening characteristics o SMAs under largeamplitudes an improved Graesser and Cozzarelli model ispresented In the present model the backstress expression ismodi1047297ed by adding a special term to capture the martensitichardening characteristic o SMA under large amplitudes Temodi1047297ed model is o the orm
907317 = 983131 minus | | 1048616907317 minus 10486171103925minus1 1048616907317 minus 1048617983133 (983095)
F983145983143983157983154983141 983094 Mechanical properties o RSMAD as a unction o prestrain and displacement amplitude (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
+ 1048667 minus M sgn ()1048669 [ ( )]times 1048667 983080|| minus M 9830811048669983165
(983096)
Te third term in (983090) is used to contribute to the back-stress on the ascending branch o the hysteresis in a way thatallows or the martensitic hardening M is the martensite1047297nish strain and are material constants controlling themartensitic hardening curve sgn() is the signum unctiongiven by
Figure 983090 shows the stress-strain curves o superelasticnitinol wires predicted by the improved Graesser and Coz-zarelli model versus experimental data at different strain
levels Te characteristic parameters used in the models are = 39500MPa = 385MPa = 001 907317 = 114 = 0001 = 550 = 3 M = 005 = 42500and = 3 Te superelastic nitinol wires are 983088983093 mm indiameter with a composition o approximately 983093983088983097 Ni and
983092983097983089 i Under zero external stress the martensite startand 1047297nish temperatures (10383891038389) and the austenite startand 1047297nish temperatures (1103925 1103925) measured by differential
scanning calorimeter (DSC) are minus983095983091∘C minus983093983093∘C minus983090983091∘C and983093∘C respectively Te uniaxial tension test o the superelasticnitinol wires was carried out using an electromechanicaluniversal testing machine at room temperature o 983090983088∘C Tenitinol wire samples with a 983089983088983088 mm test length between thetwo custom-made grips were subjected to triangular cyclicloading under different strain amplitudes Te strains werecalculated rom the elongation measured by a 983093983088 mm gagelength extensometer with the stress calculated rom the axialorce which was measured by a 983089983088 KN load cell Prior to
F983145983143983157983154983141 983095 Hysteresis loops o the RSMAD at different loading requencies and displacement amplitudes (983088983094 mm predisplacement 983090983088∘Ctemperature)
testing the nitinol SMA specimens were cycled 983090983088 times
at 983094 strain amplitude and 983089983090 times 983089983088minus3 sminus1 strain rate by a ldquotrainingrdquo process to reach a steady-state condition Teexperimental data in Figure 983090 are the results o cyclic tests on
the superelastic nitinol wire at 983089983090 times 983089983088minus3 sminus1 strain rate with983089 to 983096 strain levels As shown in Figure 983090 the hysteresisloops based on the improved Graesser and Cozzarelli model
and experimental data match with close accuracy Moreoverthe improved model can accurately re1047298ect the martensitichardening characteristic o SMAs under large amplitudes
3 An Innovative SMA Damper DesignExperiment and Numerical Simulation
983091983089 Recentering SMA Damper Design By utilizing the energy dissipating and recentering eatures o superelastic nitinolSMA an innovative damper is designed As shown inFigure 983091 the damper consists o outerand inner cylinderslefand right pull plates superelastic SMA wires retaining plate
prestrain adjusting plate adjusting bolt 1047297xed bolt push-pullrod grip end caps and connecting 1047297tting In this dampersuperelastic nitinol wiresare the key components thatprovideboth damping and sel-centering abilities
Te damper will be connected to a structure via its push-pull rod and the connecting 1047297tting Te prestrain o thesuperelastic wires can be adjusted by the prestrain adjusting
plate and the adjusting bolt Te con1047297guration o the dampershown in Figure 983091 is in its equilibrium position Te speci1047297cdesign o the damper allows the push-pull rod to move inboth lef and right directions and return to its equilibriumposition when the load is removed (sel-centering) Duringthis cyclic process the damper provides damping attributedto the hysteretic property o the superelastic wires
983091983090 Experimental ests
983091983090983089 Setup and Program An SMA damper based on thedesign presented in Section 983091983089 is abricated o assess theperormance o the SMA damper cyclic tests were carried
F983145983143983157983154983141 983096 Mechanical properties o RSMAD as a unction o loading requencies and displacement amplitudes (983088983094 mm predisplacement983090983088∘C temperature)
out Te SMA damper is 983090983089983088 mm in length with a diametero 983089983088983088 mm and a stroke o plusmn983097983090 mm (the maximum allowablestrain or superelastic nitinol wires is 983096) Four superelasticnitinol wires o a length o 983089983089983093 mm and a diameter o 983088983093 mmare used
ests were conducted using an MS 983096983089983088 machine with a983089983088983088 KN load cell at room temperature o 983090983088∘C Te layout o the test system is shown in Figure 983092 Te damper was testedwith different prestrains at different loading requenciesand at various amplitudes During the tests both orce anddisplacement are recorded
Prior to the installation each nitinol wire was cycled 983090983088
times at 983094 strain with 983089983090 times 983089983088minus3 sminus1 strain rate to minimizethe accumulation o residual strain and reach a steady-statecondition Te scheme o the tests is described as ollows
(983089) Without prestrain the damper was subjected tocyclic loading at 983088983088983093 Hz requency with displacement
amplitudes o 983090983091 mm (983090 o total length) 983091983092983093 mm(983091 o total length) and 983092983094 mm (983092 o total length)respectively
(983090) Step (983089) was repeated with prestrains o 983089 (983089983089983093 mmpredisplacement) 983090 (983090983091 mm predisplacement) and
983092 (983092983094 mm predisplacement) respectively
(983091) With 983088983093 prestrain (about 983088983094 mm predisplace-ment) the damper was subjected to cyclic loading at983088983088983089 Hz loading requency with displacement ampli-tudes o 983090983091 mm 983091983092983093 mm 983092983094 mm and 983093983095983093mmrespectively
(983092) Step (983091) was repeated with loading requencies o 983088983088983093 Hz 983088983089 Hz 983088983093 Hz 983089 Hz and 983090 Hz respectively
o describe the perormance o RSMAD as a unctiono prestrains loading requencies and displacement ampli-tudes some important mechanical properties were calcu-lated including the secant stiffness
F983145983143983157983154983141 983097 Comparison between experimental and numerical 1047297tting
curves o RSMAD
per cycle the restoring orce at peak displacement percycle1038389 andthe equivalent viscous damping ratio eq whichis expressed as
eq = 22 (983089983088)
where is the displacement amplitude o the cycle
983091983090983090 Experimental Results Figure 983093 shows the hysteresisloops o RSMAD at different prestrains and displacementamplitudes Te tests were carried out at 983088983088983093 Hz requency o loading and room temperature o 983090983088∘C As seen romFigure 983093 the SMA damper shows double-1047298ag hystereticbehavior without any residual strain
Figure 983094 shows the mechanical properties o RSMAD as aunction o prestrain and displacement amplitude As we cansee in Figure 983094 the greater the amplitude is the greater theenergy dissipation per cycle and restoring orce are Howeverthe secant stiffness reduces markedly while increasing theamplitude With the increasing o the predisplacement theenergy dissipation per cycle decreases and restoring orceand the secant stiffness increase at large displacement Teeffectiveness o a damper is generally measured by the
equivalent viscous damping ratio With the increasing o thepredisplacement the equivalent damping ratio reduces Temost important 1047297nding is that when the predisplacementis less than 983090983091 mm (983090 prestrain) the equivalent dampingratio increased with the increasing o the amplitude howeverwhen the predisplacement is 983092983094 mm (983092 prestrain) themaximum o the equivalent damping ratio is at 983090983091 mm (983090prestrain) Tis is because the maximum o the equivalentdamping ratioo the Nii SMA specimens is atabout 983094 totalstrain as noted in [983089983088]
Figure 983095 shows the hysteresis loops o RSMAD with983088983094 mm predisplacement at different loading requencies anddisplacement amplitudes at the temperature o 983090983088∘C Figure 983096
shows mechanical properties o RSMAD as a unction o requency o loading and displacement amplitude As wecan see in Figures 983095 and 983096 the energy dissipation percycle and the equivalent damping decrease as the loadingrequency increases in the range o 983088983088983089ndash983088983093 Hz but arenot much sensitive to requencies greater than 983088983093 Hz Te
restoring orce and the secant stiffness increase slightly as theloading requency increasesin the total range o experimentalrequency
983091983091 Numerical Simulation Based on the improved Graesserand Cozzarelli model o SMA wire a theoretic model o theSMA damper is developed Te differential equations o themodel are given as
= 0 983131 minus | |
minus
(1103925minus1) 1048616 minus
1048617983133
= 0 in + 907317|| er () [ (minus )]+ 1048667 minus M sgn ()1048669times [ ( )] 1048667 983080|| minus M 9830811048669983165
(983089983089)
where is restoring orce is displacement is back-orce0 is initial stiffness 907317 M and and areconstants controlling the size o the hysteresis loop in is theinelastic displacement and in = minus 0 er () () andsgn() are respectively the error unction the step unctionand the signum unction which have already been listed inSection 983090
Figure 983097 shows the comparison o experimental resultswith numerical prediction based on the theoretical modelat different displacement amplitudes Te parameters o theconstitutive equation used in this studyto simulate the behav-iors o RSMAD are given as ollows 0 = 380Nmm =330N = 005 907317 = 21 = 00001 = 3 = 2M = 575mm = 42500 and = 3 o accurately simulate the hysteresis behavior the above parameters weredirectly obtained rom the cyclic test results o the SMAdamper according to the parametersrsquo meanings and roles Te
values also can be converted through the section area andthe length o Nii wires However there is slight difference
between the two parameter groups Tis is possible becauseo the effect o loading conditions on the cyclic behavior o Nii wires As can be seen in Figure 983097 numerical predictionsagree well with the experimental results
able 983089 shows the comparison o the experimental dataand numerical results respectively o the energy dissipationper cycle the secant stiffness and the equivalent viscousdamping As can be seen in able 983089 the maximum differenceso energy dissipation per cycle secant stiffness and equiva-lent viscous damping are 983093983088 983089983090 and 983093983089 respectivelyTese results indicate that the mechanical behavior o theSMA damper is well predicted by the numerical model which
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983089 Stress-strain diagrams o Nii shape memory alloy (a) SME lt 1038389 (b) superelasticity 1103925 lt lt 10383891038389
0
100
200
300
400
500
600
700
800
Experimental data
Te improved Graesser and Cozzarelli
000 001 002 003 004 005 006 007 008 009
S t r e s s 1038389
( M P a
)
Strain
F983145983143983157983154983141 983090 Stress-strain curves o superelastic nitinol wires
Shape memory alloys [983089983091] are a class o novel unctionalmaterials that possess unique properties including shape
memory effect (SME) superelasticity effect (SE) extraor-dinary atigue resistance high corrosion resistance highdampingcharacteristics and temperature-dependent Youngrsquosmodulus At a low temperature SMAs exhibit the SMEmdashresidual deormations can be recovered by heating the mate-rial above the austenite 1047297nish temperature as shown inFigure 983089(a) At a higher temperature SMAs exhibit the SEas shown in Figure 983089(b) In the superelastic phase SMAs areinitially austenitic However upon loading stress-inducedmartensite is ormed Upon unloading the martensite revertsto austenite at a lower stress level resulting in the hystereticbehavior Tese properties make them ideal candidates orseismic energy dissipation devices in structural engineering
A signi1047297cant number o research studies have beenconducted in an effort to use SMAs orapplications in seismicresistant design and structural retro1047297t in the past decade(eg [983089983092ndash983090983092]) Wilde et al [983089983092] proposed a smart isolationsystem combining a laminated rubber bearing with a devicemade o SMA or highway bridges Teir analytical resultsshow that the isolation system can limit displacement anddissipate energy or earthquake mitigation Dolce et al [983089983093]developed two amilies o SMA-based energy dissipating andrecentering braces or seismic vibration control o buildingsand bridges as outcomes o the MANSIDE project (Memory
Alloys or New Seismic Isolation and Energy DissipationDevices) o assess the effectiveness o SMA braces toreduce the seismic response o reinorced concrete (RC)ramed structures shaking table tests o a 983089983091983091-scale three-story two-bay RC plane rame which was designed orlow seismicity and low ductility according to the Europeanseismic code were carried out by Dolce et al [983089983094] Teirexperimental results show that the SMA braces can enhanceseismic perormances at least comparable to those providedby steel braces while having an additional sel-centeringeature Indirli et al [983089983095] retro1047297tted historic buildings usingsuperelastic SMA tie bars to enhance its seismic resistancecapacities DesRoches and Delemont [983089983096] and Andrawes
and Desroches [983089983097] evaluated the efficacy o superelasticnitinol bars as restrainers to reduce the risk o collapserom unseating o bridge superstructures at the hinges Tey ound that the SMA bars are effective in limiting relativehinge displacements in typical multiple rame bridges Liet al [983090983088] investigated the vibration mitigation o a stay cable provided with one superelastic SMA damper Teanalytical results show that the SMA damper can reducecable vibration signi1047297cantly and the control effectivenessis in1047298uenced by SMA damper parameters and locationsZhang and Zhu [983090983089] developed reusable hysteretic damper(RHD) based on superelastic nitinol stranded wires andtheir numerical analysis indicated the effectiveness o RHD
F983145983143983157983154983141 983091 Diagram o RSMAD
F983145983143983157983154983141 983092 Photograph o experimental setup
in passive seismic response control o structures Ocel et al[983090983090]and McCormick et al [983090983091] investigated beam-columnconnections using SMA bars Teir studies show that SMAcan enhance the seismic perormance o the connectionsParulekaret al[983090983092] proposed a damper deviceusing austeniteNii wires Te device is tested and validated using a thermo-mechanical model o SMA taking into account the residualmartensite accumulation Perormance o the structure withSMA dampers is compared with that o the same structurewith yielding dampers
Previous works show that SMAs are o promise in struc-tural engineering particularly as energy dissipation compo-nents or seismic protection However signi1047297cant research
is still needed In Particular designing new types o SMA-based passive seismic devices which possess not only energy dissipation and recentering capabilities but also simple con-1047297guration or easy installation in the practical engineering isstill a challenge
Tis paper presents an innovative recentering shapememory alloy damper (RSMAD) or seismic structural pro-tection Te damper is simple in design and easy to imple-ment Superelastic nitinol wires were utilized in the damperas kernel energy dissipating components Cyclic tensile-compressive tests on the damper model with various prestrainunder different loading requencies and displacements wereconducted o assess the effectiveness o the damper or
structural seismic protection nonlinear time history analyseson a ten-story steel rame subjected to representative earth-quake ground motions with and without the dampers wereperormed
2 Constitutive Equation of Superelastic SMA Wire
With the wide applications o SMAs in different 1047297elds mod-eling o the peculiar mechanical behavior o SMAs such asSME and superelasticity has been an active area o researchover the past decades So ar many constitutive models orSMA have been developed [983090983093ndash983091983091] Tese models describethe thermomechanical thermoelectrical and thermochem-ical behaviors o SMAs however most o them are too com-plex to be convenient or practical application in earthquakeengineering In this paper a relatively simple model devel-oped by Graesser and Cozzarelli [983091983092] is adopted Tis model
is an extension o a one-dimensional strain rate independentmodel or hysteretic behavior proposed by Ozdemir [983091983093]Teequation is given as
907317 = 852059 minus | | 1048616907317 minus 10486171103925852061 (983089)
where 907317 and are the one-dimensional stress and the one-dimensional strain respectively is the initial elastic modu-lus is the yield stress is a constant assumed any positiveodd real value controlling the sharpnesso transition rom theelastic state to the phase transormation and denote thetime derivative o the stress and strain respectively and isthe one-dimensional back stress given by
= in + 907317|| er () [ (minus )]983165 (983090)
where 907317 and are material constants controlling the typeand size o the hysteresis the amount o elastic recovery dur-ing unloading and the slope o the unloading stress plateaurespectively When 907317 = 0 the model is purely martensiticWhen 907317 gt 0 the model predicts the superelastic behavior is a constant controlling the slope o the 907317 minus curve in theinelastic range given by
F983145983143983157983154983141 983093 Hysteresis loops o the RSMAD at different prestrains and displacement amplitudes (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
in is the inelastic strain given by
in = minus 907317 (983092)
() is the unit step unction de1047297ned as
() = 983163+1 ge 00 lt 0 (983093)
er () is the error unction de1047297ned by
er () = 2radic int
0minus2 (983094)
Te original Graesser and Cozzarelli model has a rel-atively simple expression with the parameters that can beeasily acquired however this model excludes the martensitichardening characteristics o SMAs under large amplitudeswhich are critical or structural saety protection underextreme events
o overcome the limitation o the original model Wildeet al [983089983092] extended the Graesser and Cozzarelli model by dividing the ull loop into our parts adding two termswith six parameters into (983089) Te Wilde model was utilizedto simulate the cyclic behaviors o SMA devices in otherresearches [983090983089]
In the ollowing in order to accurately predict the cyclic
behavior o a superelastic SMA device especially capture themartensitic hardening characteristics o SMAs under largeamplitudes an improved Graesser and Cozzarelli model ispresented In the present model the backstress expression ismodi1047297ed by adding a special term to capture the martensitichardening characteristic o SMA under large amplitudes Temodi1047297ed model is o the orm
907317 = 983131 minus | | 1048616907317 minus 10486171103925minus1 1048616907317 minus 1048617983133 (983095)
F983145983143983157983154983141 983094 Mechanical properties o RSMAD as a unction o prestrain and displacement amplitude (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
+ 1048667 minus M sgn ()1048669 [ ( )]times 1048667 983080|| minus M 9830811048669983165
(983096)
Te third term in (983090) is used to contribute to the back-stress on the ascending branch o the hysteresis in a way thatallows or the martensitic hardening M is the martensite1047297nish strain and are material constants controlling themartensitic hardening curve sgn() is the signum unctiongiven by
Figure 983090 shows the stress-strain curves o superelasticnitinol wires predicted by the improved Graesser and Coz-zarelli model versus experimental data at different strain
levels Te characteristic parameters used in the models are = 39500MPa = 385MPa = 001 907317 = 114 = 0001 = 550 = 3 M = 005 = 42500and = 3 Te superelastic nitinol wires are 983088983093 mm indiameter with a composition o approximately 983093983088983097 Ni and
983092983097983089 i Under zero external stress the martensite startand 1047297nish temperatures (10383891038389) and the austenite startand 1047297nish temperatures (1103925 1103925) measured by differential
scanning calorimeter (DSC) are minus983095983091∘C minus983093983093∘C minus983090983091∘C and983093∘C respectively Te uniaxial tension test o the superelasticnitinol wires was carried out using an electromechanicaluniversal testing machine at room temperature o 983090983088∘C Tenitinol wire samples with a 983089983088983088 mm test length between thetwo custom-made grips were subjected to triangular cyclicloading under different strain amplitudes Te strains werecalculated rom the elongation measured by a 983093983088 mm gagelength extensometer with the stress calculated rom the axialorce which was measured by a 983089983088 KN load cell Prior to
F983145983143983157983154983141 983095 Hysteresis loops o the RSMAD at different loading requencies and displacement amplitudes (983088983094 mm predisplacement 983090983088∘Ctemperature)
testing the nitinol SMA specimens were cycled 983090983088 times
at 983094 strain amplitude and 983089983090 times 983089983088minus3 sminus1 strain rate by a ldquotrainingrdquo process to reach a steady-state condition Teexperimental data in Figure 983090 are the results o cyclic tests on
the superelastic nitinol wire at 983089983090 times 983089983088minus3 sminus1 strain rate with983089 to 983096 strain levels As shown in Figure 983090 the hysteresisloops based on the improved Graesser and Cozzarelli model
and experimental data match with close accuracy Moreoverthe improved model can accurately re1047298ect the martensitichardening characteristic o SMAs under large amplitudes
3 An Innovative SMA Damper DesignExperiment and Numerical Simulation
983091983089 Recentering SMA Damper Design By utilizing the energy dissipating and recentering eatures o superelastic nitinolSMA an innovative damper is designed As shown inFigure 983091 the damper consists o outerand inner cylinderslefand right pull plates superelastic SMA wires retaining plate
prestrain adjusting plate adjusting bolt 1047297xed bolt push-pullrod grip end caps and connecting 1047297tting In this dampersuperelastic nitinol wiresare the key components thatprovideboth damping and sel-centering abilities
Te damper will be connected to a structure via its push-pull rod and the connecting 1047297tting Te prestrain o thesuperelastic wires can be adjusted by the prestrain adjusting
plate and the adjusting bolt Te con1047297guration o the dampershown in Figure 983091 is in its equilibrium position Te speci1047297cdesign o the damper allows the push-pull rod to move inboth lef and right directions and return to its equilibriumposition when the load is removed (sel-centering) Duringthis cyclic process the damper provides damping attributedto the hysteretic property o the superelastic wires
983091983090 Experimental ests
983091983090983089 Setup and Program An SMA damper based on thedesign presented in Section 983091983089 is abricated o assess theperormance o the SMA damper cyclic tests were carried
F983145983143983157983154983141 983096 Mechanical properties o RSMAD as a unction o loading requencies and displacement amplitudes (983088983094 mm predisplacement983090983088∘C temperature)
out Te SMA damper is 983090983089983088 mm in length with a diametero 983089983088983088 mm and a stroke o plusmn983097983090 mm (the maximum allowablestrain or superelastic nitinol wires is 983096) Four superelasticnitinol wires o a length o 983089983089983093 mm and a diameter o 983088983093 mmare used
ests were conducted using an MS 983096983089983088 machine with a983089983088983088 KN load cell at room temperature o 983090983088∘C Te layout o the test system is shown in Figure 983092 Te damper was testedwith different prestrains at different loading requenciesand at various amplitudes During the tests both orce anddisplacement are recorded
Prior to the installation each nitinol wire was cycled 983090983088
times at 983094 strain with 983089983090 times 983089983088minus3 sminus1 strain rate to minimizethe accumulation o residual strain and reach a steady-statecondition Te scheme o the tests is described as ollows
(983089) Without prestrain the damper was subjected tocyclic loading at 983088983088983093 Hz requency with displacement
amplitudes o 983090983091 mm (983090 o total length) 983091983092983093 mm(983091 o total length) and 983092983094 mm (983092 o total length)respectively
(983090) Step (983089) was repeated with prestrains o 983089 (983089983089983093 mmpredisplacement) 983090 (983090983091 mm predisplacement) and
983092 (983092983094 mm predisplacement) respectively
(983091) With 983088983093 prestrain (about 983088983094 mm predisplace-ment) the damper was subjected to cyclic loading at983088983088983089 Hz loading requency with displacement ampli-tudes o 983090983091 mm 983091983092983093 mm 983092983094 mm and 983093983095983093mmrespectively
(983092) Step (983091) was repeated with loading requencies o 983088983088983093 Hz 983088983089 Hz 983088983093 Hz 983089 Hz and 983090 Hz respectively
o describe the perormance o RSMAD as a unctiono prestrains loading requencies and displacement ampli-tudes some important mechanical properties were calcu-lated including the secant stiffness
F983145983143983157983154983141 983097 Comparison between experimental and numerical 1047297tting
curves o RSMAD
per cycle the restoring orce at peak displacement percycle1038389 andthe equivalent viscous damping ratio eq whichis expressed as
eq = 22 (983089983088)
where is the displacement amplitude o the cycle
983091983090983090 Experimental Results Figure 983093 shows the hysteresisloops o RSMAD at different prestrains and displacementamplitudes Te tests were carried out at 983088983088983093 Hz requency o loading and room temperature o 983090983088∘C As seen romFigure 983093 the SMA damper shows double-1047298ag hystereticbehavior without any residual strain
Figure 983094 shows the mechanical properties o RSMAD as aunction o prestrain and displacement amplitude As we cansee in Figure 983094 the greater the amplitude is the greater theenergy dissipation per cycle and restoring orce are Howeverthe secant stiffness reduces markedly while increasing theamplitude With the increasing o the predisplacement theenergy dissipation per cycle decreases and restoring orceand the secant stiffness increase at large displacement Teeffectiveness o a damper is generally measured by the
equivalent viscous damping ratio With the increasing o thepredisplacement the equivalent damping ratio reduces Temost important 1047297nding is that when the predisplacementis less than 983090983091 mm (983090 prestrain) the equivalent dampingratio increased with the increasing o the amplitude howeverwhen the predisplacement is 983092983094 mm (983092 prestrain) themaximum o the equivalent damping ratio is at 983090983091 mm (983090prestrain) Tis is because the maximum o the equivalentdamping ratioo the Nii SMA specimens is atabout 983094 totalstrain as noted in [983089983088]
Figure 983095 shows the hysteresis loops o RSMAD with983088983094 mm predisplacement at different loading requencies anddisplacement amplitudes at the temperature o 983090983088∘C Figure 983096
shows mechanical properties o RSMAD as a unction o requency o loading and displacement amplitude As wecan see in Figures 983095 and 983096 the energy dissipation percycle and the equivalent damping decrease as the loadingrequency increases in the range o 983088983088983089ndash983088983093 Hz but arenot much sensitive to requencies greater than 983088983093 Hz Te
restoring orce and the secant stiffness increase slightly as theloading requency increasesin the total range o experimentalrequency
983091983091 Numerical Simulation Based on the improved Graesserand Cozzarelli model o SMA wire a theoretic model o theSMA damper is developed Te differential equations o themodel are given as
= 0 983131 minus | |
minus
(1103925minus1) 1048616 minus
1048617983133
= 0 in + 907317|| er () [ (minus )]+ 1048667 minus M sgn ()1048669times [ ( )] 1048667 983080|| minus M 9830811048669983165
(983089983089)
where is restoring orce is displacement is back-orce0 is initial stiffness 907317 M and and areconstants controlling the size o the hysteresis loop in is theinelastic displacement and in = minus 0 er () () andsgn() are respectively the error unction the step unctionand the signum unction which have already been listed inSection 983090
Figure 983097 shows the comparison o experimental resultswith numerical prediction based on the theoretical modelat different displacement amplitudes Te parameters o theconstitutive equation used in this studyto simulate the behav-iors o RSMAD are given as ollows 0 = 380Nmm =330N = 005 907317 = 21 = 00001 = 3 = 2M = 575mm = 42500 and = 3 o accurately simulate the hysteresis behavior the above parameters weredirectly obtained rom the cyclic test results o the SMAdamper according to the parametersrsquo meanings and roles Te
values also can be converted through the section area andthe length o Nii wires However there is slight difference
between the two parameter groups Tis is possible becauseo the effect o loading conditions on the cyclic behavior o Nii wires As can be seen in Figure 983097 numerical predictionsagree well with the experimental results
able 983089 shows the comparison o the experimental dataand numerical results respectively o the energy dissipationper cycle the secant stiffness and the equivalent viscousdamping As can be seen in able 983089 the maximum differenceso energy dissipation per cycle secant stiffness and equiva-lent viscous damping are 983093983088 983089983090 and 983093983089 respectivelyTese results indicate that the mechanical behavior o theSMA damper is well predicted by the numerical model which
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983091 Diagram o RSMAD
F983145983143983157983154983141 983092 Photograph o experimental setup
in passive seismic response control o structures Ocel et al[983090983090]and McCormick et al [983090983091] investigated beam-columnconnections using SMA bars Teir studies show that SMAcan enhance the seismic perormance o the connectionsParulekaret al[983090983092] proposed a damper deviceusing austeniteNii wires Te device is tested and validated using a thermo-mechanical model o SMA taking into account the residualmartensite accumulation Perormance o the structure withSMA dampers is compared with that o the same structurewith yielding dampers
Previous works show that SMAs are o promise in struc-tural engineering particularly as energy dissipation compo-nents or seismic protection However signi1047297cant research
is still needed In Particular designing new types o SMA-based passive seismic devices which possess not only energy dissipation and recentering capabilities but also simple con-1047297guration or easy installation in the practical engineering isstill a challenge
Tis paper presents an innovative recentering shapememory alloy damper (RSMAD) or seismic structural pro-tection Te damper is simple in design and easy to imple-ment Superelastic nitinol wires were utilized in the damperas kernel energy dissipating components Cyclic tensile-compressive tests on the damper model with various prestrainunder different loading requencies and displacements wereconducted o assess the effectiveness o the damper or
structural seismic protection nonlinear time history analyseson a ten-story steel rame subjected to representative earth-quake ground motions with and without the dampers wereperormed
2 Constitutive Equation of Superelastic SMA Wire
With the wide applications o SMAs in different 1047297elds mod-eling o the peculiar mechanical behavior o SMAs such asSME and superelasticity has been an active area o researchover the past decades So ar many constitutive models orSMA have been developed [983090983093ndash983091983091] Tese models describethe thermomechanical thermoelectrical and thermochem-ical behaviors o SMAs however most o them are too com-plex to be convenient or practical application in earthquakeengineering In this paper a relatively simple model devel-oped by Graesser and Cozzarelli [983091983092] is adopted Tis model
is an extension o a one-dimensional strain rate independentmodel or hysteretic behavior proposed by Ozdemir [983091983093]Teequation is given as
907317 = 852059 minus | | 1048616907317 minus 10486171103925852061 (983089)
where 907317 and are the one-dimensional stress and the one-dimensional strain respectively is the initial elastic modu-lus is the yield stress is a constant assumed any positiveodd real value controlling the sharpnesso transition rom theelastic state to the phase transormation and denote thetime derivative o the stress and strain respectively and isthe one-dimensional back stress given by
= in + 907317|| er () [ (minus )]983165 (983090)
where 907317 and are material constants controlling the typeand size o the hysteresis the amount o elastic recovery dur-ing unloading and the slope o the unloading stress plateaurespectively When 907317 = 0 the model is purely martensiticWhen 907317 gt 0 the model predicts the superelastic behavior is a constant controlling the slope o the 907317 minus curve in theinelastic range given by
F983145983143983157983154983141 983093 Hysteresis loops o the RSMAD at different prestrains and displacement amplitudes (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
in is the inelastic strain given by
in = minus 907317 (983092)
() is the unit step unction de1047297ned as
() = 983163+1 ge 00 lt 0 (983093)
er () is the error unction de1047297ned by
er () = 2radic int
0minus2 (983094)
Te original Graesser and Cozzarelli model has a rel-atively simple expression with the parameters that can beeasily acquired however this model excludes the martensitichardening characteristics o SMAs under large amplitudeswhich are critical or structural saety protection underextreme events
o overcome the limitation o the original model Wildeet al [983089983092] extended the Graesser and Cozzarelli model by dividing the ull loop into our parts adding two termswith six parameters into (983089) Te Wilde model was utilizedto simulate the cyclic behaviors o SMA devices in otherresearches [983090983089]
In the ollowing in order to accurately predict the cyclic
behavior o a superelastic SMA device especially capture themartensitic hardening characteristics o SMAs under largeamplitudes an improved Graesser and Cozzarelli model ispresented In the present model the backstress expression ismodi1047297ed by adding a special term to capture the martensitichardening characteristic o SMA under large amplitudes Temodi1047297ed model is o the orm
907317 = 983131 minus | | 1048616907317 minus 10486171103925minus1 1048616907317 minus 1048617983133 (983095)
F983145983143983157983154983141 983094 Mechanical properties o RSMAD as a unction o prestrain and displacement amplitude (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
+ 1048667 minus M sgn ()1048669 [ ( )]times 1048667 983080|| minus M 9830811048669983165
(983096)
Te third term in (983090) is used to contribute to the back-stress on the ascending branch o the hysteresis in a way thatallows or the martensitic hardening M is the martensite1047297nish strain and are material constants controlling themartensitic hardening curve sgn() is the signum unctiongiven by
Figure 983090 shows the stress-strain curves o superelasticnitinol wires predicted by the improved Graesser and Coz-zarelli model versus experimental data at different strain
levels Te characteristic parameters used in the models are = 39500MPa = 385MPa = 001 907317 = 114 = 0001 = 550 = 3 M = 005 = 42500and = 3 Te superelastic nitinol wires are 983088983093 mm indiameter with a composition o approximately 983093983088983097 Ni and
983092983097983089 i Under zero external stress the martensite startand 1047297nish temperatures (10383891038389) and the austenite startand 1047297nish temperatures (1103925 1103925) measured by differential
scanning calorimeter (DSC) are minus983095983091∘C minus983093983093∘C minus983090983091∘C and983093∘C respectively Te uniaxial tension test o the superelasticnitinol wires was carried out using an electromechanicaluniversal testing machine at room temperature o 983090983088∘C Tenitinol wire samples with a 983089983088983088 mm test length between thetwo custom-made grips were subjected to triangular cyclicloading under different strain amplitudes Te strains werecalculated rom the elongation measured by a 983093983088 mm gagelength extensometer with the stress calculated rom the axialorce which was measured by a 983089983088 KN load cell Prior to
F983145983143983157983154983141 983095 Hysteresis loops o the RSMAD at different loading requencies and displacement amplitudes (983088983094 mm predisplacement 983090983088∘Ctemperature)
testing the nitinol SMA specimens were cycled 983090983088 times
at 983094 strain amplitude and 983089983090 times 983089983088minus3 sminus1 strain rate by a ldquotrainingrdquo process to reach a steady-state condition Teexperimental data in Figure 983090 are the results o cyclic tests on
the superelastic nitinol wire at 983089983090 times 983089983088minus3 sminus1 strain rate with983089 to 983096 strain levels As shown in Figure 983090 the hysteresisloops based on the improved Graesser and Cozzarelli model
and experimental data match with close accuracy Moreoverthe improved model can accurately re1047298ect the martensitichardening characteristic o SMAs under large amplitudes
3 An Innovative SMA Damper DesignExperiment and Numerical Simulation
983091983089 Recentering SMA Damper Design By utilizing the energy dissipating and recentering eatures o superelastic nitinolSMA an innovative damper is designed As shown inFigure 983091 the damper consists o outerand inner cylinderslefand right pull plates superelastic SMA wires retaining plate
prestrain adjusting plate adjusting bolt 1047297xed bolt push-pullrod grip end caps and connecting 1047297tting In this dampersuperelastic nitinol wiresare the key components thatprovideboth damping and sel-centering abilities
Te damper will be connected to a structure via its push-pull rod and the connecting 1047297tting Te prestrain o thesuperelastic wires can be adjusted by the prestrain adjusting
plate and the adjusting bolt Te con1047297guration o the dampershown in Figure 983091 is in its equilibrium position Te speci1047297cdesign o the damper allows the push-pull rod to move inboth lef and right directions and return to its equilibriumposition when the load is removed (sel-centering) Duringthis cyclic process the damper provides damping attributedto the hysteretic property o the superelastic wires
983091983090 Experimental ests
983091983090983089 Setup and Program An SMA damper based on thedesign presented in Section 983091983089 is abricated o assess theperormance o the SMA damper cyclic tests were carried
F983145983143983157983154983141 983096 Mechanical properties o RSMAD as a unction o loading requencies and displacement amplitudes (983088983094 mm predisplacement983090983088∘C temperature)
out Te SMA damper is 983090983089983088 mm in length with a diametero 983089983088983088 mm and a stroke o plusmn983097983090 mm (the maximum allowablestrain or superelastic nitinol wires is 983096) Four superelasticnitinol wires o a length o 983089983089983093 mm and a diameter o 983088983093 mmare used
ests were conducted using an MS 983096983089983088 machine with a983089983088983088 KN load cell at room temperature o 983090983088∘C Te layout o the test system is shown in Figure 983092 Te damper was testedwith different prestrains at different loading requenciesand at various amplitudes During the tests both orce anddisplacement are recorded
Prior to the installation each nitinol wire was cycled 983090983088
times at 983094 strain with 983089983090 times 983089983088minus3 sminus1 strain rate to minimizethe accumulation o residual strain and reach a steady-statecondition Te scheme o the tests is described as ollows
(983089) Without prestrain the damper was subjected tocyclic loading at 983088983088983093 Hz requency with displacement
amplitudes o 983090983091 mm (983090 o total length) 983091983092983093 mm(983091 o total length) and 983092983094 mm (983092 o total length)respectively
(983090) Step (983089) was repeated with prestrains o 983089 (983089983089983093 mmpredisplacement) 983090 (983090983091 mm predisplacement) and
983092 (983092983094 mm predisplacement) respectively
(983091) With 983088983093 prestrain (about 983088983094 mm predisplace-ment) the damper was subjected to cyclic loading at983088983088983089 Hz loading requency with displacement ampli-tudes o 983090983091 mm 983091983092983093 mm 983092983094 mm and 983093983095983093mmrespectively
(983092) Step (983091) was repeated with loading requencies o 983088983088983093 Hz 983088983089 Hz 983088983093 Hz 983089 Hz and 983090 Hz respectively
o describe the perormance o RSMAD as a unctiono prestrains loading requencies and displacement ampli-tudes some important mechanical properties were calcu-lated including the secant stiffness
F983145983143983157983154983141 983097 Comparison between experimental and numerical 1047297tting
curves o RSMAD
per cycle the restoring orce at peak displacement percycle1038389 andthe equivalent viscous damping ratio eq whichis expressed as
eq = 22 (983089983088)
where is the displacement amplitude o the cycle
983091983090983090 Experimental Results Figure 983093 shows the hysteresisloops o RSMAD at different prestrains and displacementamplitudes Te tests were carried out at 983088983088983093 Hz requency o loading and room temperature o 983090983088∘C As seen romFigure 983093 the SMA damper shows double-1047298ag hystereticbehavior without any residual strain
Figure 983094 shows the mechanical properties o RSMAD as aunction o prestrain and displacement amplitude As we cansee in Figure 983094 the greater the amplitude is the greater theenergy dissipation per cycle and restoring orce are Howeverthe secant stiffness reduces markedly while increasing theamplitude With the increasing o the predisplacement theenergy dissipation per cycle decreases and restoring orceand the secant stiffness increase at large displacement Teeffectiveness o a damper is generally measured by the
equivalent viscous damping ratio With the increasing o thepredisplacement the equivalent damping ratio reduces Temost important 1047297nding is that when the predisplacementis less than 983090983091 mm (983090 prestrain) the equivalent dampingratio increased with the increasing o the amplitude howeverwhen the predisplacement is 983092983094 mm (983092 prestrain) themaximum o the equivalent damping ratio is at 983090983091 mm (983090prestrain) Tis is because the maximum o the equivalentdamping ratioo the Nii SMA specimens is atabout 983094 totalstrain as noted in [983089983088]
Figure 983095 shows the hysteresis loops o RSMAD with983088983094 mm predisplacement at different loading requencies anddisplacement amplitudes at the temperature o 983090983088∘C Figure 983096
shows mechanical properties o RSMAD as a unction o requency o loading and displacement amplitude As wecan see in Figures 983095 and 983096 the energy dissipation percycle and the equivalent damping decrease as the loadingrequency increases in the range o 983088983088983089ndash983088983093 Hz but arenot much sensitive to requencies greater than 983088983093 Hz Te
restoring orce and the secant stiffness increase slightly as theloading requency increasesin the total range o experimentalrequency
983091983091 Numerical Simulation Based on the improved Graesserand Cozzarelli model o SMA wire a theoretic model o theSMA damper is developed Te differential equations o themodel are given as
= 0 983131 minus | |
minus
(1103925minus1) 1048616 minus
1048617983133
= 0 in + 907317|| er () [ (minus )]+ 1048667 minus M sgn ()1048669times [ ( )] 1048667 983080|| minus M 9830811048669983165
(983089983089)
where is restoring orce is displacement is back-orce0 is initial stiffness 907317 M and and areconstants controlling the size o the hysteresis loop in is theinelastic displacement and in = minus 0 er () () andsgn() are respectively the error unction the step unctionand the signum unction which have already been listed inSection 983090
Figure 983097 shows the comparison o experimental resultswith numerical prediction based on the theoretical modelat different displacement amplitudes Te parameters o theconstitutive equation used in this studyto simulate the behav-iors o RSMAD are given as ollows 0 = 380Nmm =330N = 005 907317 = 21 = 00001 = 3 = 2M = 575mm = 42500 and = 3 o accurately simulate the hysteresis behavior the above parameters weredirectly obtained rom the cyclic test results o the SMAdamper according to the parametersrsquo meanings and roles Te
values also can be converted through the section area andthe length o Nii wires However there is slight difference
between the two parameter groups Tis is possible becauseo the effect o loading conditions on the cyclic behavior o Nii wires As can be seen in Figure 983097 numerical predictionsagree well with the experimental results
able 983089 shows the comparison o the experimental dataand numerical results respectively o the energy dissipationper cycle the secant stiffness and the equivalent viscousdamping As can be seen in able 983089 the maximum differenceso energy dissipation per cycle secant stiffness and equiva-lent viscous damping are 983093983088 983089983090 and 983093983089 respectivelyTese results indicate that the mechanical behavior o theSMA damper is well predicted by the numerical model which
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983093 Hysteresis loops o the RSMAD at different prestrains and displacement amplitudes (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
in is the inelastic strain given by
in = minus 907317 (983092)
() is the unit step unction de1047297ned as
() = 983163+1 ge 00 lt 0 (983093)
er () is the error unction de1047297ned by
er () = 2radic int
0minus2 (983094)
Te original Graesser and Cozzarelli model has a rel-atively simple expression with the parameters that can beeasily acquired however this model excludes the martensitichardening characteristics o SMAs under large amplitudeswhich are critical or structural saety protection underextreme events
o overcome the limitation o the original model Wildeet al [983089983092] extended the Graesser and Cozzarelli model by dividing the ull loop into our parts adding two termswith six parameters into (983089) Te Wilde model was utilizedto simulate the cyclic behaviors o SMA devices in otherresearches [983090983089]
In the ollowing in order to accurately predict the cyclic
behavior o a superelastic SMA device especially capture themartensitic hardening characteristics o SMAs under largeamplitudes an improved Graesser and Cozzarelli model ispresented In the present model the backstress expression ismodi1047297ed by adding a special term to capture the martensitichardening characteristic o SMA under large amplitudes Temodi1047297ed model is o the orm
907317 = 983131 minus | | 1048616907317 minus 10486171103925minus1 1048616907317 minus 1048617983133 (983095)
F983145983143983157983154983141 983094 Mechanical properties o RSMAD as a unction o prestrain and displacement amplitude (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
+ 1048667 minus M sgn ()1048669 [ ( )]times 1048667 983080|| minus M 9830811048669983165
(983096)
Te third term in (983090) is used to contribute to the back-stress on the ascending branch o the hysteresis in a way thatallows or the martensitic hardening M is the martensite1047297nish strain and are material constants controlling themartensitic hardening curve sgn() is the signum unctiongiven by
Figure 983090 shows the stress-strain curves o superelasticnitinol wires predicted by the improved Graesser and Coz-zarelli model versus experimental data at different strain
levels Te characteristic parameters used in the models are = 39500MPa = 385MPa = 001 907317 = 114 = 0001 = 550 = 3 M = 005 = 42500and = 3 Te superelastic nitinol wires are 983088983093 mm indiameter with a composition o approximately 983093983088983097 Ni and
983092983097983089 i Under zero external stress the martensite startand 1047297nish temperatures (10383891038389) and the austenite startand 1047297nish temperatures (1103925 1103925) measured by differential
scanning calorimeter (DSC) are minus983095983091∘C minus983093983093∘C minus983090983091∘C and983093∘C respectively Te uniaxial tension test o the superelasticnitinol wires was carried out using an electromechanicaluniversal testing machine at room temperature o 983090983088∘C Tenitinol wire samples with a 983089983088983088 mm test length between thetwo custom-made grips were subjected to triangular cyclicloading under different strain amplitudes Te strains werecalculated rom the elongation measured by a 983093983088 mm gagelength extensometer with the stress calculated rom the axialorce which was measured by a 983089983088 KN load cell Prior to
F983145983143983157983154983141 983095 Hysteresis loops o the RSMAD at different loading requencies and displacement amplitudes (983088983094 mm predisplacement 983090983088∘Ctemperature)
testing the nitinol SMA specimens were cycled 983090983088 times
at 983094 strain amplitude and 983089983090 times 983089983088minus3 sminus1 strain rate by a ldquotrainingrdquo process to reach a steady-state condition Teexperimental data in Figure 983090 are the results o cyclic tests on
the superelastic nitinol wire at 983089983090 times 983089983088minus3 sminus1 strain rate with983089 to 983096 strain levels As shown in Figure 983090 the hysteresisloops based on the improved Graesser and Cozzarelli model
and experimental data match with close accuracy Moreoverthe improved model can accurately re1047298ect the martensitichardening characteristic o SMAs under large amplitudes
3 An Innovative SMA Damper DesignExperiment and Numerical Simulation
983091983089 Recentering SMA Damper Design By utilizing the energy dissipating and recentering eatures o superelastic nitinolSMA an innovative damper is designed As shown inFigure 983091 the damper consists o outerand inner cylinderslefand right pull plates superelastic SMA wires retaining plate
prestrain adjusting plate adjusting bolt 1047297xed bolt push-pullrod grip end caps and connecting 1047297tting In this dampersuperelastic nitinol wiresare the key components thatprovideboth damping and sel-centering abilities
Te damper will be connected to a structure via its push-pull rod and the connecting 1047297tting Te prestrain o thesuperelastic wires can be adjusted by the prestrain adjusting
plate and the adjusting bolt Te con1047297guration o the dampershown in Figure 983091 is in its equilibrium position Te speci1047297cdesign o the damper allows the push-pull rod to move inboth lef and right directions and return to its equilibriumposition when the load is removed (sel-centering) Duringthis cyclic process the damper provides damping attributedto the hysteretic property o the superelastic wires
983091983090 Experimental ests
983091983090983089 Setup and Program An SMA damper based on thedesign presented in Section 983091983089 is abricated o assess theperormance o the SMA damper cyclic tests were carried
F983145983143983157983154983141 983096 Mechanical properties o RSMAD as a unction o loading requencies and displacement amplitudes (983088983094 mm predisplacement983090983088∘C temperature)
out Te SMA damper is 983090983089983088 mm in length with a diametero 983089983088983088 mm and a stroke o plusmn983097983090 mm (the maximum allowablestrain or superelastic nitinol wires is 983096) Four superelasticnitinol wires o a length o 983089983089983093 mm and a diameter o 983088983093 mmare used
ests were conducted using an MS 983096983089983088 machine with a983089983088983088 KN load cell at room temperature o 983090983088∘C Te layout o the test system is shown in Figure 983092 Te damper was testedwith different prestrains at different loading requenciesand at various amplitudes During the tests both orce anddisplacement are recorded
Prior to the installation each nitinol wire was cycled 983090983088
times at 983094 strain with 983089983090 times 983089983088minus3 sminus1 strain rate to minimizethe accumulation o residual strain and reach a steady-statecondition Te scheme o the tests is described as ollows
(983089) Without prestrain the damper was subjected tocyclic loading at 983088983088983093 Hz requency with displacement
amplitudes o 983090983091 mm (983090 o total length) 983091983092983093 mm(983091 o total length) and 983092983094 mm (983092 o total length)respectively
(983090) Step (983089) was repeated with prestrains o 983089 (983089983089983093 mmpredisplacement) 983090 (983090983091 mm predisplacement) and
983092 (983092983094 mm predisplacement) respectively
(983091) With 983088983093 prestrain (about 983088983094 mm predisplace-ment) the damper was subjected to cyclic loading at983088983088983089 Hz loading requency with displacement ampli-tudes o 983090983091 mm 983091983092983093 mm 983092983094 mm and 983093983095983093mmrespectively
(983092) Step (983091) was repeated with loading requencies o 983088983088983093 Hz 983088983089 Hz 983088983093 Hz 983089 Hz and 983090 Hz respectively
o describe the perormance o RSMAD as a unctiono prestrains loading requencies and displacement ampli-tudes some important mechanical properties were calcu-lated including the secant stiffness
F983145983143983157983154983141 983097 Comparison between experimental and numerical 1047297tting
curves o RSMAD
per cycle the restoring orce at peak displacement percycle1038389 andthe equivalent viscous damping ratio eq whichis expressed as
eq = 22 (983089983088)
where is the displacement amplitude o the cycle
983091983090983090 Experimental Results Figure 983093 shows the hysteresisloops o RSMAD at different prestrains and displacementamplitudes Te tests were carried out at 983088983088983093 Hz requency o loading and room temperature o 983090983088∘C As seen romFigure 983093 the SMA damper shows double-1047298ag hystereticbehavior without any residual strain
Figure 983094 shows the mechanical properties o RSMAD as aunction o prestrain and displacement amplitude As we cansee in Figure 983094 the greater the amplitude is the greater theenergy dissipation per cycle and restoring orce are Howeverthe secant stiffness reduces markedly while increasing theamplitude With the increasing o the predisplacement theenergy dissipation per cycle decreases and restoring orceand the secant stiffness increase at large displacement Teeffectiveness o a damper is generally measured by the
equivalent viscous damping ratio With the increasing o thepredisplacement the equivalent damping ratio reduces Temost important 1047297nding is that when the predisplacementis less than 983090983091 mm (983090 prestrain) the equivalent dampingratio increased with the increasing o the amplitude howeverwhen the predisplacement is 983092983094 mm (983092 prestrain) themaximum o the equivalent damping ratio is at 983090983091 mm (983090prestrain) Tis is because the maximum o the equivalentdamping ratioo the Nii SMA specimens is atabout 983094 totalstrain as noted in [983089983088]
Figure 983095 shows the hysteresis loops o RSMAD with983088983094 mm predisplacement at different loading requencies anddisplacement amplitudes at the temperature o 983090983088∘C Figure 983096
shows mechanical properties o RSMAD as a unction o requency o loading and displacement amplitude As wecan see in Figures 983095 and 983096 the energy dissipation percycle and the equivalent damping decrease as the loadingrequency increases in the range o 983088983088983089ndash983088983093 Hz but arenot much sensitive to requencies greater than 983088983093 Hz Te
restoring orce and the secant stiffness increase slightly as theloading requency increasesin the total range o experimentalrequency
983091983091 Numerical Simulation Based on the improved Graesserand Cozzarelli model o SMA wire a theoretic model o theSMA damper is developed Te differential equations o themodel are given as
= 0 983131 minus | |
minus
(1103925minus1) 1048616 minus
1048617983133
= 0 in + 907317|| er () [ (minus )]+ 1048667 minus M sgn ()1048669times [ ( )] 1048667 983080|| minus M 9830811048669983165
(983089983089)
where is restoring orce is displacement is back-orce0 is initial stiffness 907317 M and and areconstants controlling the size o the hysteresis loop in is theinelastic displacement and in = minus 0 er () () andsgn() are respectively the error unction the step unctionand the signum unction which have already been listed inSection 983090
Figure 983097 shows the comparison o experimental resultswith numerical prediction based on the theoretical modelat different displacement amplitudes Te parameters o theconstitutive equation used in this studyto simulate the behav-iors o RSMAD are given as ollows 0 = 380Nmm =330N = 005 907317 = 21 = 00001 = 3 = 2M = 575mm = 42500 and = 3 o accurately simulate the hysteresis behavior the above parameters weredirectly obtained rom the cyclic test results o the SMAdamper according to the parametersrsquo meanings and roles Te
values also can be converted through the section area andthe length o Nii wires However there is slight difference
between the two parameter groups Tis is possible becauseo the effect o loading conditions on the cyclic behavior o Nii wires As can be seen in Figure 983097 numerical predictionsagree well with the experimental results
able 983089 shows the comparison o the experimental dataand numerical results respectively o the energy dissipationper cycle the secant stiffness and the equivalent viscousdamping As can be seen in able 983089 the maximum differenceso energy dissipation per cycle secant stiffness and equiva-lent viscous damping are 983093983088 983089983090 and 983093983089 respectivelyTese results indicate that the mechanical behavior o theSMA damper is well predicted by the numerical model which
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983094 Mechanical properties o RSMAD as a unction o prestrain and displacement amplitude (983088983088983093 Hz requency o loading 983090983088∘Ctemperature)
+ 1048667 minus M sgn ()1048669 [ ( )]times 1048667 983080|| minus M 9830811048669983165
(983096)
Te third term in (983090) is used to contribute to the back-stress on the ascending branch o the hysteresis in a way thatallows or the martensitic hardening M is the martensite1047297nish strain and are material constants controlling themartensitic hardening curve sgn() is the signum unctiongiven by
Figure 983090 shows the stress-strain curves o superelasticnitinol wires predicted by the improved Graesser and Coz-zarelli model versus experimental data at different strain
levels Te characteristic parameters used in the models are = 39500MPa = 385MPa = 001 907317 = 114 = 0001 = 550 = 3 M = 005 = 42500and = 3 Te superelastic nitinol wires are 983088983093 mm indiameter with a composition o approximately 983093983088983097 Ni and
983092983097983089 i Under zero external stress the martensite startand 1047297nish temperatures (10383891038389) and the austenite startand 1047297nish temperatures (1103925 1103925) measured by differential
scanning calorimeter (DSC) are minus983095983091∘C minus983093983093∘C minus983090983091∘C and983093∘C respectively Te uniaxial tension test o the superelasticnitinol wires was carried out using an electromechanicaluniversal testing machine at room temperature o 983090983088∘C Tenitinol wire samples with a 983089983088983088 mm test length between thetwo custom-made grips were subjected to triangular cyclicloading under different strain amplitudes Te strains werecalculated rom the elongation measured by a 983093983088 mm gagelength extensometer with the stress calculated rom the axialorce which was measured by a 983089983088 KN load cell Prior to
F983145983143983157983154983141 983095 Hysteresis loops o the RSMAD at different loading requencies and displacement amplitudes (983088983094 mm predisplacement 983090983088∘Ctemperature)
testing the nitinol SMA specimens were cycled 983090983088 times
at 983094 strain amplitude and 983089983090 times 983089983088minus3 sminus1 strain rate by a ldquotrainingrdquo process to reach a steady-state condition Teexperimental data in Figure 983090 are the results o cyclic tests on
the superelastic nitinol wire at 983089983090 times 983089983088minus3 sminus1 strain rate with983089 to 983096 strain levels As shown in Figure 983090 the hysteresisloops based on the improved Graesser and Cozzarelli model
and experimental data match with close accuracy Moreoverthe improved model can accurately re1047298ect the martensitichardening characteristic o SMAs under large amplitudes
3 An Innovative SMA Damper DesignExperiment and Numerical Simulation
983091983089 Recentering SMA Damper Design By utilizing the energy dissipating and recentering eatures o superelastic nitinolSMA an innovative damper is designed As shown inFigure 983091 the damper consists o outerand inner cylinderslefand right pull plates superelastic SMA wires retaining plate
prestrain adjusting plate adjusting bolt 1047297xed bolt push-pullrod grip end caps and connecting 1047297tting In this dampersuperelastic nitinol wiresare the key components thatprovideboth damping and sel-centering abilities
Te damper will be connected to a structure via its push-pull rod and the connecting 1047297tting Te prestrain o thesuperelastic wires can be adjusted by the prestrain adjusting
plate and the adjusting bolt Te con1047297guration o the dampershown in Figure 983091 is in its equilibrium position Te speci1047297cdesign o the damper allows the push-pull rod to move inboth lef and right directions and return to its equilibriumposition when the load is removed (sel-centering) Duringthis cyclic process the damper provides damping attributedto the hysteretic property o the superelastic wires
983091983090 Experimental ests
983091983090983089 Setup and Program An SMA damper based on thedesign presented in Section 983091983089 is abricated o assess theperormance o the SMA damper cyclic tests were carried
F983145983143983157983154983141 983096 Mechanical properties o RSMAD as a unction o loading requencies and displacement amplitudes (983088983094 mm predisplacement983090983088∘C temperature)
out Te SMA damper is 983090983089983088 mm in length with a diametero 983089983088983088 mm and a stroke o plusmn983097983090 mm (the maximum allowablestrain or superelastic nitinol wires is 983096) Four superelasticnitinol wires o a length o 983089983089983093 mm and a diameter o 983088983093 mmare used
ests were conducted using an MS 983096983089983088 machine with a983089983088983088 KN load cell at room temperature o 983090983088∘C Te layout o the test system is shown in Figure 983092 Te damper was testedwith different prestrains at different loading requenciesand at various amplitudes During the tests both orce anddisplacement are recorded
Prior to the installation each nitinol wire was cycled 983090983088
times at 983094 strain with 983089983090 times 983089983088minus3 sminus1 strain rate to minimizethe accumulation o residual strain and reach a steady-statecondition Te scheme o the tests is described as ollows
(983089) Without prestrain the damper was subjected tocyclic loading at 983088983088983093 Hz requency with displacement
amplitudes o 983090983091 mm (983090 o total length) 983091983092983093 mm(983091 o total length) and 983092983094 mm (983092 o total length)respectively
(983090) Step (983089) was repeated with prestrains o 983089 (983089983089983093 mmpredisplacement) 983090 (983090983091 mm predisplacement) and
983092 (983092983094 mm predisplacement) respectively
(983091) With 983088983093 prestrain (about 983088983094 mm predisplace-ment) the damper was subjected to cyclic loading at983088983088983089 Hz loading requency with displacement ampli-tudes o 983090983091 mm 983091983092983093 mm 983092983094 mm and 983093983095983093mmrespectively
(983092) Step (983091) was repeated with loading requencies o 983088983088983093 Hz 983088983089 Hz 983088983093 Hz 983089 Hz and 983090 Hz respectively
o describe the perormance o RSMAD as a unctiono prestrains loading requencies and displacement ampli-tudes some important mechanical properties were calcu-lated including the secant stiffness
F983145983143983157983154983141 983097 Comparison between experimental and numerical 1047297tting
curves o RSMAD
per cycle the restoring orce at peak displacement percycle1038389 andthe equivalent viscous damping ratio eq whichis expressed as
eq = 22 (983089983088)
where is the displacement amplitude o the cycle
983091983090983090 Experimental Results Figure 983093 shows the hysteresisloops o RSMAD at different prestrains and displacementamplitudes Te tests were carried out at 983088983088983093 Hz requency o loading and room temperature o 983090983088∘C As seen romFigure 983093 the SMA damper shows double-1047298ag hystereticbehavior without any residual strain
Figure 983094 shows the mechanical properties o RSMAD as aunction o prestrain and displacement amplitude As we cansee in Figure 983094 the greater the amplitude is the greater theenergy dissipation per cycle and restoring orce are Howeverthe secant stiffness reduces markedly while increasing theamplitude With the increasing o the predisplacement theenergy dissipation per cycle decreases and restoring orceand the secant stiffness increase at large displacement Teeffectiveness o a damper is generally measured by the
equivalent viscous damping ratio With the increasing o thepredisplacement the equivalent damping ratio reduces Temost important 1047297nding is that when the predisplacementis less than 983090983091 mm (983090 prestrain) the equivalent dampingratio increased with the increasing o the amplitude howeverwhen the predisplacement is 983092983094 mm (983092 prestrain) themaximum o the equivalent damping ratio is at 983090983091 mm (983090prestrain) Tis is because the maximum o the equivalentdamping ratioo the Nii SMA specimens is atabout 983094 totalstrain as noted in [983089983088]
Figure 983095 shows the hysteresis loops o RSMAD with983088983094 mm predisplacement at different loading requencies anddisplacement amplitudes at the temperature o 983090983088∘C Figure 983096
shows mechanical properties o RSMAD as a unction o requency o loading and displacement amplitude As wecan see in Figures 983095 and 983096 the energy dissipation percycle and the equivalent damping decrease as the loadingrequency increases in the range o 983088983088983089ndash983088983093 Hz but arenot much sensitive to requencies greater than 983088983093 Hz Te
restoring orce and the secant stiffness increase slightly as theloading requency increasesin the total range o experimentalrequency
983091983091 Numerical Simulation Based on the improved Graesserand Cozzarelli model o SMA wire a theoretic model o theSMA damper is developed Te differential equations o themodel are given as
= 0 983131 minus | |
minus
(1103925minus1) 1048616 minus
1048617983133
= 0 in + 907317|| er () [ (minus )]+ 1048667 minus M sgn ()1048669times [ ( )] 1048667 983080|| minus M 9830811048669983165
(983089983089)
where is restoring orce is displacement is back-orce0 is initial stiffness 907317 M and and areconstants controlling the size o the hysteresis loop in is theinelastic displacement and in = minus 0 er () () andsgn() are respectively the error unction the step unctionand the signum unction which have already been listed inSection 983090
Figure 983097 shows the comparison o experimental resultswith numerical prediction based on the theoretical modelat different displacement amplitudes Te parameters o theconstitutive equation used in this studyto simulate the behav-iors o RSMAD are given as ollows 0 = 380Nmm =330N = 005 907317 = 21 = 00001 = 3 = 2M = 575mm = 42500 and = 3 o accurately simulate the hysteresis behavior the above parameters weredirectly obtained rom the cyclic test results o the SMAdamper according to the parametersrsquo meanings and roles Te
values also can be converted through the section area andthe length o Nii wires However there is slight difference
between the two parameter groups Tis is possible becauseo the effect o loading conditions on the cyclic behavior o Nii wires As can be seen in Figure 983097 numerical predictionsagree well with the experimental results
able 983089 shows the comparison o the experimental dataand numerical results respectively o the energy dissipationper cycle the secant stiffness and the equivalent viscousdamping As can be seen in able 983089 the maximum differenceso energy dissipation per cycle secant stiffness and equiva-lent viscous damping are 983093983088 983089983090 and 983093983089 respectivelyTese results indicate that the mechanical behavior o theSMA damper is well predicted by the numerical model which
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983095 Hysteresis loops o the RSMAD at different loading requencies and displacement amplitudes (983088983094 mm predisplacement 983090983088∘Ctemperature)
testing the nitinol SMA specimens were cycled 983090983088 times
at 983094 strain amplitude and 983089983090 times 983089983088minus3 sminus1 strain rate by a ldquotrainingrdquo process to reach a steady-state condition Teexperimental data in Figure 983090 are the results o cyclic tests on
the superelastic nitinol wire at 983089983090 times 983089983088minus3 sminus1 strain rate with983089 to 983096 strain levels As shown in Figure 983090 the hysteresisloops based on the improved Graesser and Cozzarelli model
and experimental data match with close accuracy Moreoverthe improved model can accurately re1047298ect the martensitichardening characteristic o SMAs under large amplitudes
3 An Innovative SMA Damper DesignExperiment and Numerical Simulation
983091983089 Recentering SMA Damper Design By utilizing the energy dissipating and recentering eatures o superelastic nitinolSMA an innovative damper is designed As shown inFigure 983091 the damper consists o outerand inner cylinderslefand right pull plates superelastic SMA wires retaining plate
prestrain adjusting plate adjusting bolt 1047297xed bolt push-pullrod grip end caps and connecting 1047297tting In this dampersuperelastic nitinol wiresare the key components thatprovideboth damping and sel-centering abilities
Te damper will be connected to a structure via its push-pull rod and the connecting 1047297tting Te prestrain o thesuperelastic wires can be adjusted by the prestrain adjusting
plate and the adjusting bolt Te con1047297guration o the dampershown in Figure 983091 is in its equilibrium position Te speci1047297cdesign o the damper allows the push-pull rod to move inboth lef and right directions and return to its equilibriumposition when the load is removed (sel-centering) Duringthis cyclic process the damper provides damping attributedto the hysteretic property o the superelastic wires
983091983090 Experimental ests
983091983090983089 Setup and Program An SMA damper based on thedesign presented in Section 983091983089 is abricated o assess theperormance o the SMA damper cyclic tests were carried
F983145983143983157983154983141 983096 Mechanical properties o RSMAD as a unction o loading requencies and displacement amplitudes (983088983094 mm predisplacement983090983088∘C temperature)
out Te SMA damper is 983090983089983088 mm in length with a diametero 983089983088983088 mm and a stroke o plusmn983097983090 mm (the maximum allowablestrain or superelastic nitinol wires is 983096) Four superelasticnitinol wires o a length o 983089983089983093 mm and a diameter o 983088983093 mmare used
ests were conducted using an MS 983096983089983088 machine with a983089983088983088 KN load cell at room temperature o 983090983088∘C Te layout o the test system is shown in Figure 983092 Te damper was testedwith different prestrains at different loading requenciesand at various amplitudes During the tests both orce anddisplacement are recorded
Prior to the installation each nitinol wire was cycled 983090983088
times at 983094 strain with 983089983090 times 983089983088minus3 sminus1 strain rate to minimizethe accumulation o residual strain and reach a steady-statecondition Te scheme o the tests is described as ollows
(983089) Without prestrain the damper was subjected tocyclic loading at 983088983088983093 Hz requency with displacement
amplitudes o 983090983091 mm (983090 o total length) 983091983092983093 mm(983091 o total length) and 983092983094 mm (983092 o total length)respectively
(983090) Step (983089) was repeated with prestrains o 983089 (983089983089983093 mmpredisplacement) 983090 (983090983091 mm predisplacement) and
983092 (983092983094 mm predisplacement) respectively
(983091) With 983088983093 prestrain (about 983088983094 mm predisplace-ment) the damper was subjected to cyclic loading at983088983088983089 Hz loading requency with displacement ampli-tudes o 983090983091 mm 983091983092983093 mm 983092983094 mm and 983093983095983093mmrespectively
(983092) Step (983091) was repeated with loading requencies o 983088983088983093 Hz 983088983089 Hz 983088983093 Hz 983089 Hz and 983090 Hz respectively
o describe the perormance o RSMAD as a unctiono prestrains loading requencies and displacement ampli-tudes some important mechanical properties were calcu-lated including the secant stiffness
F983145983143983157983154983141 983097 Comparison between experimental and numerical 1047297tting
curves o RSMAD
per cycle the restoring orce at peak displacement percycle1038389 andthe equivalent viscous damping ratio eq whichis expressed as
eq = 22 (983089983088)
where is the displacement amplitude o the cycle
983091983090983090 Experimental Results Figure 983093 shows the hysteresisloops o RSMAD at different prestrains and displacementamplitudes Te tests were carried out at 983088983088983093 Hz requency o loading and room temperature o 983090983088∘C As seen romFigure 983093 the SMA damper shows double-1047298ag hystereticbehavior without any residual strain
Figure 983094 shows the mechanical properties o RSMAD as aunction o prestrain and displacement amplitude As we cansee in Figure 983094 the greater the amplitude is the greater theenergy dissipation per cycle and restoring orce are Howeverthe secant stiffness reduces markedly while increasing theamplitude With the increasing o the predisplacement theenergy dissipation per cycle decreases and restoring orceand the secant stiffness increase at large displacement Teeffectiveness o a damper is generally measured by the
equivalent viscous damping ratio With the increasing o thepredisplacement the equivalent damping ratio reduces Temost important 1047297nding is that when the predisplacementis less than 983090983091 mm (983090 prestrain) the equivalent dampingratio increased with the increasing o the amplitude howeverwhen the predisplacement is 983092983094 mm (983092 prestrain) themaximum o the equivalent damping ratio is at 983090983091 mm (983090prestrain) Tis is because the maximum o the equivalentdamping ratioo the Nii SMA specimens is atabout 983094 totalstrain as noted in [983089983088]
Figure 983095 shows the hysteresis loops o RSMAD with983088983094 mm predisplacement at different loading requencies anddisplacement amplitudes at the temperature o 983090983088∘C Figure 983096
shows mechanical properties o RSMAD as a unction o requency o loading and displacement amplitude As wecan see in Figures 983095 and 983096 the energy dissipation percycle and the equivalent damping decrease as the loadingrequency increases in the range o 983088983088983089ndash983088983093 Hz but arenot much sensitive to requencies greater than 983088983093 Hz Te
restoring orce and the secant stiffness increase slightly as theloading requency increasesin the total range o experimentalrequency
983091983091 Numerical Simulation Based on the improved Graesserand Cozzarelli model o SMA wire a theoretic model o theSMA damper is developed Te differential equations o themodel are given as
= 0 983131 minus | |
minus
(1103925minus1) 1048616 minus
1048617983133
= 0 in + 907317|| er () [ (minus )]+ 1048667 minus M sgn ()1048669times [ ( )] 1048667 983080|| minus M 9830811048669983165
(983089983089)
where is restoring orce is displacement is back-orce0 is initial stiffness 907317 M and and areconstants controlling the size o the hysteresis loop in is theinelastic displacement and in = minus 0 er () () andsgn() are respectively the error unction the step unctionand the signum unction which have already been listed inSection 983090
Figure 983097 shows the comparison o experimental resultswith numerical prediction based on the theoretical modelat different displacement amplitudes Te parameters o theconstitutive equation used in this studyto simulate the behav-iors o RSMAD are given as ollows 0 = 380Nmm =330N = 005 907317 = 21 = 00001 = 3 = 2M = 575mm = 42500 and = 3 o accurately simulate the hysteresis behavior the above parameters weredirectly obtained rom the cyclic test results o the SMAdamper according to the parametersrsquo meanings and roles Te
values also can be converted through the section area andthe length o Nii wires However there is slight difference
between the two parameter groups Tis is possible becauseo the effect o loading conditions on the cyclic behavior o Nii wires As can be seen in Figure 983097 numerical predictionsagree well with the experimental results
able 983089 shows the comparison o the experimental dataand numerical results respectively o the energy dissipationper cycle the secant stiffness and the equivalent viscousdamping As can be seen in able 983089 the maximum differenceso energy dissipation per cycle secant stiffness and equiva-lent viscous damping are 983093983088 983089983090 and 983093983089 respectivelyTese results indicate that the mechanical behavior o theSMA damper is well predicted by the numerical model which
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983096 Mechanical properties o RSMAD as a unction o loading requencies and displacement amplitudes (983088983094 mm predisplacement983090983088∘C temperature)
out Te SMA damper is 983090983089983088 mm in length with a diametero 983089983088983088 mm and a stroke o plusmn983097983090 mm (the maximum allowablestrain or superelastic nitinol wires is 983096) Four superelasticnitinol wires o a length o 983089983089983093 mm and a diameter o 983088983093 mmare used
ests were conducted using an MS 983096983089983088 machine with a983089983088983088 KN load cell at room temperature o 983090983088∘C Te layout o the test system is shown in Figure 983092 Te damper was testedwith different prestrains at different loading requenciesand at various amplitudes During the tests both orce anddisplacement are recorded
Prior to the installation each nitinol wire was cycled 983090983088
times at 983094 strain with 983089983090 times 983089983088minus3 sminus1 strain rate to minimizethe accumulation o residual strain and reach a steady-statecondition Te scheme o the tests is described as ollows
(983089) Without prestrain the damper was subjected tocyclic loading at 983088983088983093 Hz requency with displacement
amplitudes o 983090983091 mm (983090 o total length) 983091983092983093 mm(983091 o total length) and 983092983094 mm (983092 o total length)respectively
(983090) Step (983089) was repeated with prestrains o 983089 (983089983089983093 mmpredisplacement) 983090 (983090983091 mm predisplacement) and
983092 (983092983094 mm predisplacement) respectively
(983091) With 983088983093 prestrain (about 983088983094 mm predisplace-ment) the damper was subjected to cyclic loading at983088983088983089 Hz loading requency with displacement ampli-tudes o 983090983091 mm 983091983092983093 mm 983092983094 mm and 983093983095983093mmrespectively
(983092) Step (983091) was repeated with loading requencies o 983088983088983093 Hz 983088983089 Hz 983088983093 Hz 983089 Hz and 983090 Hz respectively
o describe the perormance o RSMAD as a unctiono prestrains loading requencies and displacement ampli-tudes some important mechanical properties were calcu-lated including the secant stiffness
F983145983143983157983154983141 983097 Comparison between experimental and numerical 1047297tting
curves o RSMAD
per cycle the restoring orce at peak displacement percycle1038389 andthe equivalent viscous damping ratio eq whichis expressed as
eq = 22 (983089983088)
where is the displacement amplitude o the cycle
983091983090983090 Experimental Results Figure 983093 shows the hysteresisloops o RSMAD at different prestrains and displacementamplitudes Te tests were carried out at 983088983088983093 Hz requency o loading and room temperature o 983090983088∘C As seen romFigure 983093 the SMA damper shows double-1047298ag hystereticbehavior without any residual strain
Figure 983094 shows the mechanical properties o RSMAD as aunction o prestrain and displacement amplitude As we cansee in Figure 983094 the greater the amplitude is the greater theenergy dissipation per cycle and restoring orce are Howeverthe secant stiffness reduces markedly while increasing theamplitude With the increasing o the predisplacement theenergy dissipation per cycle decreases and restoring orceand the secant stiffness increase at large displacement Teeffectiveness o a damper is generally measured by the
equivalent viscous damping ratio With the increasing o thepredisplacement the equivalent damping ratio reduces Temost important 1047297nding is that when the predisplacementis less than 983090983091 mm (983090 prestrain) the equivalent dampingratio increased with the increasing o the amplitude howeverwhen the predisplacement is 983092983094 mm (983092 prestrain) themaximum o the equivalent damping ratio is at 983090983091 mm (983090prestrain) Tis is because the maximum o the equivalentdamping ratioo the Nii SMA specimens is atabout 983094 totalstrain as noted in [983089983088]
Figure 983095 shows the hysteresis loops o RSMAD with983088983094 mm predisplacement at different loading requencies anddisplacement amplitudes at the temperature o 983090983088∘C Figure 983096
shows mechanical properties o RSMAD as a unction o requency o loading and displacement amplitude As wecan see in Figures 983095 and 983096 the energy dissipation percycle and the equivalent damping decrease as the loadingrequency increases in the range o 983088983088983089ndash983088983093 Hz but arenot much sensitive to requencies greater than 983088983093 Hz Te
restoring orce and the secant stiffness increase slightly as theloading requency increasesin the total range o experimentalrequency
983091983091 Numerical Simulation Based on the improved Graesserand Cozzarelli model o SMA wire a theoretic model o theSMA damper is developed Te differential equations o themodel are given as
= 0 983131 minus | |
minus
(1103925minus1) 1048616 minus
1048617983133
= 0 in + 907317|| er () [ (minus )]+ 1048667 minus M sgn ()1048669times [ ( )] 1048667 983080|| minus M 9830811048669983165
(983089983089)
where is restoring orce is displacement is back-orce0 is initial stiffness 907317 M and and areconstants controlling the size o the hysteresis loop in is theinelastic displacement and in = minus 0 er () () andsgn() are respectively the error unction the step unctionand the signum unction which have already been listed inSection 983090
Figure 983097 shows the comparison o experimental resultswith numerical prediction based on the theoretical modelat different displacement amplitudes Te parameters o theconstitutive equation used in this studyto simulate the behav-iors o RSMAD are given as ollows 0 = 380Nmm =330N = 005 907317 = 21 = 00001 = 3 = 2M = 575mm = 42500 and = 3 o accurately simulate the hysteresis behavior the above parameters weredirectly obtained rom the cyclic test results o the SMAdamper according to the parametersrsquo meanings and roles Te
values also can be converted through the section area andthe length o Nii wires However there is slight difference
between the two parameter groups Tis is possible becauseo the effect o loading conditions on the cyclic behavior o Nii wires As can be seen in Figure 983097 numerical predictionsagree well with the experimental results
able 983089 shows the comparison o the experimental dataand numerical results respectively o the energy dissipationper cycle the secant stiffness and the equivalent viscousdamping As can be seen in able 983089 the maximum differenceso energy dissipation per cycle secant stiffness and equiva-lent viscous damping are 983093983088 983089983090 and 983093983089 respectivelyTese results indicate that the mechanical behavior o theSMA damper is well predicted by the numerical model which
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983097 Comparison between experimental and numerical 1047297tting
curves o RSMAD
per cycle the restoring orce at peak displacement percycle1038389 andthe equivalent viscous damping ratio eq whichis expressed as
eq = 22 (983089983088)
where is the displacement amplitude o the cycle
983091983090983090 Experimental Results Figure 983093 shows the hysteresisloops o RSMAD at different prestrains and displacementamplitudes Te tests were carried out at 983088983088983093 Hz requency o loading and room temperature o 983090983088∘C As seen romFigure 983093 the SMA damper shows double-1047298ag hystereticbehavior without any residual strain
Figure 983094 shows the mechanical properties o RSMAD as aunction o prestrain and displacement amplitude As we cansee in Figure 983094 the greater the amplitude is the greater theenergy dissipation per cycle and restoring orce are Howeverthe secant stiffness reduces markedly while increasing theamplitude With the increasing o the predisplacement theenergy dissipation per cycle decreases and restoring orceand the secant stiffness increase at large displacement Teeffectiveness o a damper is generally measured by the
equivalent viscous damping ratio With the increasing o thepredisplacement the equivalent damping ratio reduces Temost important 1047297nding is that when the predisplacementis less than 983090983091 mm (983090 prestrain) the equivalent dampingratio increased with the increasing o the amplitude howeverwhen the predisplacement is 983092983094 mm (983092 prestrain) themaximum o the equivalent damping ratio is at 983090983091 mm (983090prestrain) Tis is because the maximum o the equivalentdamping ratioo the Nii SMA specimens is atabout 983094 totalstrain as noted in [983089983088]
Figure 983095 shows the hysteresis loops o RSMAD with983088983094 mm predisplacement at different loading requencies anddisplacement amplitudes at the temperature o 983090983088∘C Figure 983096
shows mechanical properties o RSMAD as a unction o requency o loading and displacement amplitude As wecan see in Figures 983095 and 983096 the energy dissipation percycle and the equivalent damping decrease as the loadingrequency increases in the range o 983088983088983089ndash983088983093 Hz but arenot much sensitive to requencies greater than 983088983093 Hz Te
restoring orce and the secant stiffness increase slightly as theloading requency increasesin the total range o experimentalrequency
983091983091 Numerical Simulation Based on the improved Graesserand Cozzarelli model o SMA wire a theoretic model o theSMA damper is developed Te differential equations o themodel are given as
= 0 983131 minus | |
minus
(1103925minus1) 1048616 minus
1048617983133
= 0 in + 907317|| er () [ (minus )]+ 1048667 minus M sgn ()1048669times [ ( )] 1048667 983080|| minus M 9830811048669983165
(983089983089)
where is restoring orce is displacement is back-orce0 is initial stiffness 907317 M and and areconstants controlling the size o the hysteresis loop in is theinelastic displacement and in = minus 0 er () () andsgn() are respectively the error unction the step unctionand the signum unction which have already been listed inSection 983090
Figure 983097 shows the comparison o experimental resultswith numerical prediction based on the theoretical modelat different displacement amplitudes Te parameters o theconstitutive equation used in this studyto simulate the behav-iors o RSMAD are given as ollows 0 = 380Nmm =330N = 005 907317 = 21 = 00001 = 3 = 2M = 575mm = 42500 and = 3 o accurately simulate the hysteresis behavior the above parameters weredirectly obtained rom the cyclic test results o the SMAdamper according to the parametersrsquo meanings and roles Te
values also can be converted through the section area andthe length o Nii wires However there is slight difference
between the two parameter groups Tis is possible becauseo the effect o loading conditions on the cyclic behavior o Nii wires As can be seen in Figure 983097 numerical predictionsagree well with the experimental results
able 983089 shows the comparison o the experimental dataand numerical results respectively o the energy dissipationper cycle the secant stiffness and the equivalent viscousdamping As can be seen in able 983089 the maximum differenceso energy dissipation per cycle secant stiffness and equiva-lent viscous damping are 983093983088 983089983090 and 983093983089 respectivelyTese results indicate that the mechanical behavior o theSMA damper is well predicted by the numerical model which
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
983137983138983148983141 983090 Parameters o the structure
Story heighth (m) Story massm (kg)
Story initial
stiffnesss (kNmm)Story yield shearsy (kN)
Story yield
displacementsy (mm)
Inelastic
stiffness ratio Damping ratio983092 m 64 times 103 983092983088 983092983088983088 983089983088 983088983088983089 983090
4 Model of Structure with SMA Dampers
Te main objective o including energy dissipating devices ina structure is to reduce structural response through energy dissipation o protect the original structural members understrong seismic loading nonlinear deormation in energy dissipating devices will be allowed In rame structures the
devices are usually incorporated in steel braces connectingtwoconsecutivestorieso thebuilding Te dynamic responseo the structure subjected to earthquake loading is governedby the ollowing equation
where 1038389 is the mass matrix is the damping coefficientmatrix is the vector o the rames restoring orce and 1038389is the vector o restoring orce resulting rom SMA dampersTe and are the structural displacement velocity andacceleration vectors respectively On the right-hand side o
the equation the vector is the in1047298uence vector and the vector is the ground motion acceleration input
With the aid o the SIMULINK module o MALAB adynamical simulation system was developed in which theWen model [983091983094] is utilized to simulate the restoring orcecurve o the steel rame structure and the improved Graesserand Cozzarelli model presented above is used or Nii SMA
damper
5 Seismic Structural Control Using SMA Dampers
In this section to assess the effectiveness o the proposedrecentering SMA dampers (RSMAD) in mitigating the seis-mic response o building structure nonlinear time history analysis on a multistory steel rame with and withoutthe dampers subjected to representative earthquake groundmotions was perormed Te improved Graesser and Coz-zarelli model or RSMAD given in Section 983091983091 was employedin this numerical study A ten-story steel moment resisting
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983089983089 Lateral displacementenvelopes (a) and roodisplacement time histories (b) with andwithoutSMA dampers under basic(moderate)ground motions
rame structure was selected or this study Te building isdesigned or a location in Beijing China Te parameters o the structure are listed in able 983090
Tree representative earthquake ground motions wereused to considering the site effect Tree earthquake groundmotions namely Imperial Valley 983089983097983092983088 El Centro LincolnSchool 983089983097983093983090 af and Beijing Hotel 983089983097983095983094 angshan wereselected Tese three ground motions represent different siteconditions According to Chinese code or seismic design
o building [983091983095] the local seismic precautionary intensity iseight degrees Te peak ground accelerations (PGA) wereadjusted to 983088983090 g and 983088983092 g corresponding to a seismic hazardlevel o 983089983088 and 983090 probability o exceedance in a 983093983088-yearperiod respectively
Simulation analysis is conducted on the bare structureand on the structure with 1047297ve or ten SMA dampers installedas shown in Figure 983089983088 Parameters o the SMA damper arelisted as ollows
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
F983145983143983157983154983141 983089983090 Lateral displacement envelopes (a) and roo displacement time histories (b) with and without SMAdampers under strong (severe)ground motions
= 0010 907317 = 034 = 00001 = 2500 = 5M = 0015 = 100000 and = 3Figures 983089983089 and 983089983090 show the lateral displacement envelopes
with and without SMA dampers under basic ground motions(983088983090 g) and strong ground motions (983088983092 g) respectively Aswe can see or most cases the lateral displacement o thestructure decreases remarkably with the introduction o theSMA dampers However the location and the number o the dampers have signi1047297cant effects on the control resultsCase 983093 in which dampers are installed in all stories is
the best or the overall structural vibration control For other983092 con1047297gurations in which 1047297ve dampers are installed indifferent stores cases 983091 and 983092 with dampers installed inalternate stories perorm better than cases 983089 and 983090 withdampers placed in consecutive stories Moreover case 983091 isbetter than case 983092 since the 1047297rst story is retro1047297tted Case 983089is slightly worse due to the whiplash effect and case 983090 isthe worst since the stiffness o the lower hal is signi1047297cantly greater than that o the upper hal o the structure Teroo displacement time histories with (case 983093) and without
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
SMA dampers under basic ground motions (983088983090 g) and strongground motions (983088983092 g) are also respectively provided inFigures 983089983089 and 983089983090 which con1047297rm that the SMA damperssigni1047297cantly reduce the structural vibration
6 Concluding Remarks
Tis paper presents the results o a study on evaluating theefficacy o using an innovative SMA-based damper to reducethe seismic response o structures o describe the hysteresisbehavior o the SMA damper an improved Graesser andCozzarelli model was proposed and veri1047297ed by the cyclictensile test on SMA wires
Cyclic tests on the SMA damper model utilizing oursuperelastic SMA wires with 983088983093 mm diameter with variousprestrains under different loading requencies and displace-ment amplitudes were carriedout Te results show satisyinghysteresis properties including both recentering and energy dissipating eatures under various conditions
A comparative study on nonlinear time history analysiso the seismic response o a ten-story steel rame with theSMA dampers was perormed Five cases were considered orthe location and the number o the dampers in the storiesTe numerical analysis results indicate that the proposedSMA damper is capable o signi1047297cantly reducing seismicresponse o structures which veri1047297es its effectiveness asenergy dissipating device or structures However it is alsoindicated that the location and number have signi1047297canteffects on the results o the response
In uture multiobjective optimization model will beproposed to obtain the number and the location o the SMAdampers andlargescale shake table tests willbe perormed on
a steel rame building with SMA dampers to prove the efficacy o these dampers in dissipating seismic energy
Acknowledgments
Tis work was unded by National Science Foundation o China (no 983093983089983089983088983096983092983090983094 and no 983092983089983089983088983092983089983088983094) China PostdoctoralScience Foundation (no 983090983088983089983088983088983092983095983089983088983088983096) and Research Fundor the Doctoral Program o Higher Education o China (no983090983088983089983088983092983089983088983089983089983090983088983088983088983097) Tese supports are greatly appreciated Teopinions expressed in this study are those o the authors anddo not necessarily re1047298ect the views o the sponsor
References
[983089] H N Li and L S Huo ldquoAdvances in structural control in civilengineering in Chinardquo Mathematical Problems in Engineering vol 983090983088983089983088 Article ID 983097983091983094983088983096983089 983090983091 pages 983090983088983089983088
[983090] G Song N Ma and H N Li ldquoApplications o shape memory alloys in civil structuresrdquo Engineering Structures vol 983090983096 no 983097pp 983089983090983094983094ndash983089983090983095983092 983090983088983088983094
[983091] SEAOC Vision 983090983088983088983088 Committee Performance-Based SeismicEngineering Structural Engineering Association o CaliorniaSacramento Cali USA 983089983097983097983093
[983092] AC-983092983088 Seismic Evaluation and Retro1047297t of Conctete BuildingsApplied echnology Council 983089983097983097983094
[983093] FEMA 983090983095983091 NEHRP Guidelines for Seismic Rehabilitation of Buildings Federal Emergency Management Agency 983089983097983097983095
[983094] Y Fujino Soong and B F Spencer Jr ldquoStructural controlbasic concepts and applicationsrdquo in Proceedings of the ASCEStructures Congress pp 983089983093ndash983089983096 Chicago Ill USA April 983089983097983097983094
[983095] B F Spencer and S Nagarajaiah ldquoState o the art o structural
controlrdquo Journal of Structural Engineering vol 983089983090983097 no 983095 pp983096983092983093ndash983096983093983094 983090983088983088983091
[983096] Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons New York NY USA 983089983097983097983095
[983097] F M Mazzolani ldquoPassive control technologies or seismic-resistantbuildings in Europerdquo Progress in Structural Engineering and Materials vol 983091 no 983091 pp 983090983095983095ndash983090983096983095 983090983088983088983089
[983089983088] M Dolce and D Cardone ldquoMechanical behaviour o SMAelements or seismic applicationsmdashpart 983090 austenite Nii wiressubjected to tensionrdquo International Journal of Mechanical Sci-ences vol 983092983091 no 983089983089 pp 983090983094983093983095ndash983090983094983095983095 983090983088983088983089
[983089983089] H N Li and X X Wu ldquoLimitations o height-to-width ratioor base-isolated buildings under earthquakerdquo Te Structural
Design of all and Special Buildings vol 983089983093 no 983091 pp 983090983095983095ndash983090983096983095983090983088983088983094
[983089983090] R Desroches J McCormick and M A Delemont ldquoCyclicproperties o superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol983089983091983088no983089 pp 983091983096ndash983092983094 983090983088983088983092
[983089983091] W Duerig K N Melton D Stockel and C M Way-man Engineering Aspects of Shape Memory Alloys ButterworthHeinemann London UK 983089983097983097983088
[983089983092] K Wilde P Gardoni and Y Fujino ldquoBase isolation systemwith shape memory alloy device or elevated highway bridgesrdquoEngineering Structures vol 983090983090 no 983091 pp 983090983090983090ndash983090983090983097 983090983088983088983088
[983089983093] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting o passive control devices based on shape memory
alloysrdquo Earthquake Engineering and Structural Dynamics vol983090983097 no 983095 pp 983097983092983093ndash983097983094983096 983090983088983088983088
[983089983094] M Dolce D Cardone F C Ponzo and C Valente ldquoShakingtable tests on reinorced concrete rames without and withpassive control systemsrdquo Earthquake Engineering and Structural Dynamics vol 983091983092 no 983089983092 pp 983089983094983096983095ndash983089983095983089983095 983090983088983088983093
[983089983095] M Indirli M G Castellano P Clemente and A MartellildquoDemo-application o shape memory alloy devices the rehabili-tation o the S Giorgio Church Bell-owerrdquo in Smart Structuresand Materials 983090983088983088983089 Smart Systems for Bridges Structures and Highways vol 983092983091983091983088 o Proceedings of SPIE pp 983090983094983090ndash983090983095983090 New-port Beach Cali USA March 983090983088983088983089
[983089983096] B Andrawes and R Desroches ldquoUnseating prevention or mul-tiple rame bridges using superelastic devicesrdquo Smart Materials
and Structures vol 983089983092 no 983091 pp S983094983088ndashS983094983095 983090983088983088983093
[983089983097] R DesRoches and M Delemont ldquoSeismic retro1047297t o simply supported bridges using shape memory alloysrdquo Engineering Structures vol 983090983092 no 983091 pp 983091983090983093ndash983091983091983090 983090983088983088983090
[983090983088] H Li M Liu and J Ou ldquoVibration mitigation o a stay cablewith one shape memory alloy damperrdquo Structural Control and Health Monitoring vol 983089983089 no 983089 pp 983090983089ndash983091983094 983090983088983088983092
[983090983089] Y Zhang and S Zhu ldquoA shape memory alloy-based reusablehysteretic damper or seismic hazard mitigationrdquo Smart Mate-rials and Structures vol 983089983094 no 983093 pp 983089983094983088983091ndash983089983094983089983091 983090983088983088983095
[983090983090] J Ocel R DesRoches R Leon et al ldquoSteel beam-columnconnections using shape memory alloysrdquo Journal of Structural Engineering vol 983089983091983088 no 983093 pp 983095983091983090ndash983095983092983088 983090983088983088983092
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
[983090983091] J McCormick R Desroches D Fugazza and F AuricchioldquoSeismic assessment o concentrically braced steel rames withshape memory alloy bracesrdquo Journal of Structural Engineering vol 983089983091983091 no 983094 pp 983096983094983090ndash983096983095983088 983090983088983088983095
[983090983092] Y M Parulekar G R Reddy K K Vazeet al ldquoSeismic responseattenuation o structures using shape memory alloy dampersrdquoStructural Control and Health Monitoring vol 983089983097 no 983089 pp 983089983088983090ndash983089983089983097 983090983088983089983090
[983090983093] K anaka ldquoA thermomechanical sketch o shape memory effect one-dimensionaltensile behaviorrdquo Res Mechanicavol983089983096no 983091 pp 983090983093983089ndash983090983094983091 983089983097983096983094
[983090983094] C Liang and C A Rogers ldquoOne-dimensional thermomechan-ical constitutive relations or shape memory materialsrdquo Journal of Intelligent Material Systems and Structures vol 983089 no 983090 pp983090983088983095ndash983090983091983092 983089983097983097983088
[983090983095] L C Brinson ldquoOne-dimensional constitutive behavior o shapememory alloys thermomechanical derivation with non-con-stant material unctions and rede1047297ned martensite internal vari-ablerdquo Journal of Intelligent Material Systems and Structures vol983092 no 983090 pp 983090983090983097ndash983090983092983090 983089983097983097983091
[983090983096] F Falk ldquoModel ree energy mechanics and thermodynamicso shape memory alloysrdquo Acta Metallurgica vol 983090983096 no 983089983090 pp983089983095983095983091ndash983089983095983096983088 983089983097983096983088
[983090983097] Q P Sun and K C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashII study o the individual phenomenardquo Journal of the Mechanicsand Physics of Solids vol 983092983089 no 983089 pp 983089983097ndash983091983091 983089983097983097983091
[983091983088] J G Boydand D C LagoudasldquoA thermodynamical constitutivemodel or shape memory materialsmdashpart I the monolithicshape memory alloyrdquo International Journal of Plasticity vol 983089983090no 983094 pp 983096983088983093ndash983096983092983090 983089983097983097983094
[983091983089] Q P Sun andK C Hwang ldquoMicromechanics modelling or theconstitutive behavior o polycrystalline shape memory alloysmdashI derivation o general relationsrdquo Journal of the Mechanics and
Physics of Solids vol 983092983089 no 983089 pp 983089ndash983089983095 983089983097983097983091[983091983090] H Qian H Li G Song and W Guo ldquoA constitutive model
or superelastic shape memory alloys considering the in1047298uenceo strain raterdquo Mathematical Problems in Engineering vol 983090983088983089983091Article ID 983090983092983096983094983095983089 983096 pages 983090983088983089983091
[983091983091] W J Ren H N Li and G Song ldquoA one-dimensional strain-ratedependent constitutive model or superelastic shape memory alloysrdquo Smart Materials and Structures vol 983089983094 no 983089 pp 983089983097983089ndash983089983097983095983090983088983088983095
[983091983092] E J Graesser and F A Cozzarelli ldquoShape-memory alloys asnew materials or aseismic isolationrdquo Journal of Engineering Mechanics vol 983089983089983095 no 983089983089 pp 983090983093983097983088ndash983090983094983088983096 983089983097983097983089
[983091983093] H Ozdemir Nonlinear transient dynamic analysis of yielding structures [PhD thesis] University o Caliornia BerkeleyCali USA 983089983097983095983094
[983091983094] Y K Wen ldquoMethod or random vibrationo hysteretic systemsrdquo Journal of the Engineering Mechanics Division vol 983089983088983090 no 983090 pp983090983092983097ndash983090983094983091 983089983097983095983094
[983091983095] GB 983093983088983088983089983089-983090983088983089983088 Code for Seismic Design of Buildings Ministry o Housing and Urban-Rural Development o the PeoplersquosRepublic o China 983090983088983089983088
![Vibration Control of Steel Jacket Platform through Shape Memory Alloys Damper · Equivalent linear elastic-viscous model of shape memory alloy for isolated structures [18] Control](https://static.documents.pub/doc/80x56/5fb076156954807de70daa39/vibration-control-of-steel-jacket-platform-through-shape-memory-alloys-damper-equivalent.jpg)
