A study on vibration isolation for wind turbine structures Chad Van der Woude, Sriram Narasimhan ⇑ University of Waterloo, Waterloo, Ontario, Canada article info Article history: Received 13 July 2012 Revised 20 October 2013 Accepted 22 December 2013 Available online 24 January 2014 Keywords: Wind turbines Base isolation abstract This paper discusses the potential use of vibration isolation to reduce the dynamic response of wind tur- bine structures, with emphasis on structural response to seismic loading. Based on the concept of partial mass isolation, vibration isolators are proposed at the top of the turbine tower, just below the nacelle. The structural idealizations of a wind turbine including a nonlinear isolation system are presented and the responses are simulated using the finite element method. A sample turbine structure is presented and subjected to coherent wind and seismic loading in order to demonstrate the effect of isolation system parameters on the structural response. A parametric study is conducted to study the effect of isolation system parameters on the response of the turbine structure, including the blades. The responses are quantified in terms of several performance indices reflecting the trade-offs associated with implementing an isolation system on flexible structures. Results show that implementing an isolation system may be beneficial for reducing certain key parameters of the turbine’s structural response, and may provide an excellent design option for the design of wind turbines in seismically active parts of the world. Ó 2014 Published by Elsevier Ltd. 1. Introduction The increasing size and ubiquity of wind turbines for power generation has led to increased concerns regarding their structural integrity, particularly as new turbine structures become larger and more flexible. Much study has been devoted to wind turbine struc- tures under wind loading, including research papers [3,6,11,12], books [2,7], and the development of computer codes, both public and proprietary. Standards have been established to provide design requirements and guidance, including IEC 61400-1 [8], ‘‘Wind tur- bines – Part 1: Design requirements’’. While the literature on the topic of wind effects on the structural responses of turbines is vast, the literature on seismic analysis of turbines is scarce. As wind tur- bines continue to be embraced in more seismically active parts of the world such as California, and the western coast of British Columbia in Canada, seismic loads are likely to govern their design. This study proposes seismic isolation to reduce the vulnerability of large wind turbines to earthquake loads, particularly near-fault earthquakes. Wind effects on turbines, their modeling, and structural control, have been active areas of research. Murtagh et al. [11] showed that an uncoupled numerical model, in which blade and tower vibration are considered separately, may provide un-conservative results under wind loading. Dueñas-Osorio and Basu [6] studied the potential unavailability of wind turbines due to excessive wind-induced accelerations, and derived fragility curves and prob- abilities of unavailability of turbines. Murtagh et al. [12] proposed and detailed the behavior of a coupled structural model of a tur- bine with a tuned mass damper (TMD) and demonstrated that the TMD could provide significant reductions in structural re- sponse. Colwell and Basu [3] demonstrated that implementing a tuned liquid column damper for offshore wind turbines could re- duce structural response and prolong fatigue life. These studies demonstrated the potential effectiveness of passive control devices for reducing structural response to wind loading and prolonging fatigue life, but did not consider seismic loading. IEC 61400-1 provides no earthquake resistance requirements for standard class wind turbines as seismic loading is not design-driving in most regions of the world. A simplified method is provided in IEC 61400-1, in which the head mass and half the tower mass are lumped at hub height and subjected to seismic acceleration consistent with the fundamental frequency of the structure. If the structure can withstand the imposed loading, no further seismic considerations are required. Otherwise, or if seis- mic loading on the blades is a concern, a more detailed analysis must be undertaken consistent with local building codes. A study of a 450 kW turbine to be installed in Greece [1] found that seismic loading was not a critical concern. However, as designers work to suppress the structural actions due to wind loading using new control systems and materials, among other advances, the relative importance of seismic loading may be increased [16]. Ongoing 0141-0296/$ - see front matter Ó 2014 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.engstruct.2013.12.028 ⇑ Corresponding author. Address: Department of Civil and Environmental Engi- neering, University of Waterloo, 200 University Ave. W., Waterloo, Ontario N2L 3G1, Canada. E-mail address: [email protected](S. Narasimhan). Engineering Structures 60 (2014) 223–234 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
A study on vibration isolation for wind turbine structures
0141-0296/$ - see front matter � 2014 Published by Elsevier Ltd.http://dx.doi.org/10.1016/j.engstruct.2013.12.028
⇑ Corresponding author. Address: Department of Civil and Environmental Engi-neering, University of Waterloo, 200 University Ave. W., Waterloo, Ontario N2L 3G1,Canada.
Chad Van der Woude, Sriram Narasimhan ⇑University of Waterloo, Waterloo, Ontario, Canada
a r t i c l e i n f o a b s t r a c t
Article history:Received 13 July 2012Revised 20 October 2013Accepted 22 December 2013Available online 24 January 2014
Keywords:Wind turbinesBase isolation
This paper discusses the potential use of vibration isolation to reduce the dynamic response of wind tur-bine structures, with emphasis on structural response to seismic loading. Based on the concept of partialmass isolation, vibration isolators are proposed at the top of the turbine tower, just below the nacelle. Thestructural idealizations of a wind turbine including a nonlinear isolation system are presented and theresponses are simulated using the finite element method. A sample turbine structure is presented andsubjected to coherent wind and seismic loading in order to demonstrate the effect of isolation systemparameters on the structural response. A parametric study is conducted to study the effect of isolationsystem parameters on the response of the turbine structure, including the blades. The responses arequantified in terms of several performance indices reflecting the trade-offs associated with implementingan isolation system on flexible structures. Results show that implementing an isolation system may bebeneficial for reducing certain key parameters of the turbine’s structural response, and may provide anexcellent design option for the design of wind turbines in seismically active parts of the world.
� 2014 Published by Elsevier Ltd.
1. Introduction
The increasing size and ubiquity of wind turbines for powergeneration has led to increased concerns regarding their structuralintegrity, particularly as new turbine structures become larger andmore flexible. Much study has been devoted to wind turbine struc-tures under wind loading, including research papers [3,6,11,12],books [2,7], and the development of computer codes, both publicand proprietary. Standards have been established to provide designrequirements and guidance, including IEC 61400-1 [8], ‘‘Wind tur-bines – Part 1: Design requirements’’. While the literature on thetopic of wind effects on the structural responses of turbines is vast,the literature on seismic analysis of turbines is scarce. As wind tur-bines continue to be embraced in more seismically active parts ofthe world such as California, and the western coast of BritishColumbia in Canada, seismic loads are likely to govern their design.This study proposes seismic isolation to reduce the vulnerability oflarge wind turbines to earthquake loads, particularly near-faultearthquakes.
Wind effects on turbines, their modeling, and structural control,have been active areas of research. Murtagh et al. [11] showed thatan uncoupled numerical model, in which blade and towervibration are considered separately, may provide un-conservative
results under wind loading. Dueñas-Osorio and Basu [6] studiedthe potential unavailability of wind turbines due to excessivewind-induced accelerations, and derived fragility curves and prob-abilities of unavailability of turbines. Murtagh et al. [12] proposedand detailed the behavior of a coupled structural model of a tur-bine with a tuned mass damper (TMD) and demonstrated thatthe TMD could provide significant reductions in structural re-sponse. Colwell and Basu [3] demonstrated that implementing atuned liquid column damper for offshore wind turbines could re-duce structural response and prolong fatigue life. These studiesdemonstrated the potential effectiveness of passive control devicesfor reducing structural response to wind loading and prolongingfatigue life, but did not consider seismic loading.
IEC 61400-1 provides no earthquake resistance requirementsfor standard class wind turbines as seismic loading is notdesign-driving in most regions of the world. A simplified methodis provided in IEC 61400-1, in which the head mass and half thetower mass are lumped at hub height and subjected to seismicacceleration consistent with the fundamental frequency of thestructure. If the structure can withstand the imposed loading, nofurther seismic considerations are required. Otherwise, or if seis-mic loading on the blades is a concern, a more detailed analysismust be undertaken consistent with local building codes. A studyof a 450 kW turbine to be installed in Greece [1] found that seismicloading was not a critical concern. However, as designers work tosuppress the structural actions due to wind loading using newcontrol systems and materials, among other advances, the relativeimportance of seismic loading may be increased [16]. Ongoing
224 C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234
research in this area includes full-scale shake table testing of windturbines [17] as well as numerical studies of seismic response [20].
Seismic (base) isolation has been studied and shown to be aneffective structural control measure to reduce the vulnerability ofbuildings to strong near-fault earthquakes [13]. In base isolation,a laterally flexible layer is created between the base of a structureand the ground, changing the fundamental mode of vibration fromone dominated by structural deformation to one dominated by alarger displacement across the isolation layer with relatively littlestructural deformation [13]. There are a great variety of base isola-tion systems such as elastomeric bearings, lead-rubber bearings(LRBs), and friction pendulum systems (FPS), which have been de-ployed effectively in many building applications [13]. However, tothe knowledge of the authors, there have been no studies devotedto base isolation for wind turbine structures.
This paper proposes isolation at the top of the tower structure,just below the nacelle, unlike traditional base isolation whichdecouples the entire structure from the ground. The proposed de-sign is conceptually similar to partial mass isolation proposed forbuilding applications [21], where only a part of the structure, forexample the roof, is isolated from the surroundings. In partial massisolation, under certain circumstances the amount of energy putinto the structural system could be increased due to the flexibilityof the structure both above and below the isolator, necessitatingcareful choice of isolation properties. With proper detailing and en-ergy dissipation, the isolation system can effectively decreasestructural response. In the proposed design, LRBs are used in con-junction with fluid viscous elements as the isolation system. Para-metric studies are conducted to demonstrate its effectiveness, andto guide in the selection of the isolation system parameters. Re-sponse to coherent wind and seismic loading in the along-winddirection is studied using numerical simulations. The model isimplemented in COMSOL Multiphysics, a finite element programwhich allows for explicit inclusion of the equations required torepresent a vibration isolator.
2. Structure and isolation system modeling
Wind turbine towers and blades are both slender in sectionheight compared to their length, and are typically idealized as Eu-ler–Bernoulli beams, with response characterized by flexuraldeformation. A typical wind turbine is shown in Fig. 1. The namingconvention used for coordinate axes in this paper is also shown inFig. 1. The displacements are represented by u, v and w, while
Di
D
Fig. 1. Typical wind turbine
rotations about the axes are represented by h with subscript repre-senting the directional sense of the rotation.
Assuming the turbine is not in operation, the structural ideali-zation is a linear one, which can be represented by the matrixequations of motion [5]
M€dþ C _dþ Kd ¼ F ð1Þ
where M, C and K are the mass, damping and stiffness matrices of thediscretized structure; d is a vector of the structure’s nodal displace-ments, with overdots representing time derivatives; and F is a vectorof nodal forces. This set of equations can be solved using modal super-position, where displacements d are transformed into generalizedcoordinates whose coefficient matrices are uncoupled. Alternately,Eq. (1) can be solved directly without coordinate transformation bynumerical time-stepping schemes such as Newmark’s method.
The above formulation is valid for a parked turbine structure,where the geometry of the system is constant. When the turbineis in operation, the blades rotate relative to the nacelle. The effectof this rotation is modeled using a periodic rotational coupling be-tween the rotating hub and the stationary nacelle, which can beexpressed through co-ordinate transformations as [18]
un ¼ ur ð2Þ
vn ¼ v r cosðxtÞ �wr sinðxtÞ ð3Þ
wn ¼ wr cosðxtÞ þ v r sinðxtÞ ð4Þ
hy;n ¼ hy;r cosðxtÞ � hz;r sinðxtÞ ð5Þ
hz;n ¼ hz;r cosðxtÞ þ hy;r sinðxtÞ ð6Þ
where the subscripts ‘‘n’’ represent the stationary nacelle and ‘‘r’’represent the rotating hub frame of reference, with displacementsand rotations as shown in Fig. 1. x represents the angular velocityof the rotor, and t represents time. Incorporating the rotation of theblades allows for the evaluation of time-varying nature of the trans-ferred forces between the hub and the nacelle.
The tower and blades are idealized as beam elements, the na-celle is idealized as a rigid element offsetting the rotor plane fromthe tower, and the mass of the nacelle and hub are lumped at hubheight. For this study, the isolator is located just below the nacelle,as shown in Fig. 2a. The isolator allows along-wind and across-wind motion of the nacelle with respect to the top of the tower.For modeling purposes, the multiple degree of freedom (MDOF)tower system is coupled to the blades, another MDOF system,
rections
isplacements
θ
θ
θ
and coordinate system.
C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234 225
through the isolation element. The isolator may have linear or non-linear properties depending on its layout, materials, anddimensions.
The vibration isolator is idealized using a Bouc–Wen model [9]whose parameters are selected to yield an approximately bilinearbehavior. The equation of motion for a single degree of freedomoscillator with linear viscous damping and Bouc–Wen hysteresisis given by:
m€xþ c _xþ FrðtÞ ¼ f ðtÞ ð7Þ
where m is the mass of the oscillator, c is the damping coefficient, Fr
is the restoring force, f is the applied external force, x is the dis-placement of the oscillator (note that x is interpreted as the defor-mation in the isolator model, which is an element of the vector x inEq. (1)), and overdots denote differentiation with respect to time.The restoring force is expressed as [9]:
FrðtÞ ¼ akixþ ð1� aÞkiz ð8Þ
where a is the ratio of post-yield to pre-yield stiffness, ki is the pre-yield stiffness, and z is the hysteretic displacement. The first term isan elastic restoring force, while the second term represents the hys-teretic contribution. The magnitude of the hysteretic variable attime t is given by the solution to the nonlinear differential equation:
where A, b, c and n are dimensionless parameters which determinethe shape of the force–displacement curve. For an isolator which isflexible in two orthogonal directions, corresponding versions of Eqs.(8) and (9) can be written for each direction. Assuming n = 2, the bi-directionally coupled hysteretic displacements are defined by theequations having zero initial condition [15], given by
where x and y refer to the displacements in the x and y directionsand zx and zy are the corresponding hysteretic displacements. Abilinear stiffness curve can be obtained by setting A equal to 1, con-straining b and c to be equal, and setting
xy ¼1
bþ c
� �1=n
ð12Þ
where xy is the yield displacement of the isolator [10]. For large val-ues of n, the model tends toward an ideal bilinear behavior with asharp transition. In this paper, where the motions of the top andbottom of the isolator are time-dependent, the displacement, veloc-ity and acceleration of the oscillator correspond to the differencebetween those at the top and bottom. The finite-element idealiza-tion along with the rotational coupling and the isolation systemmodeling (modeled as a constraint) is shown in Fig. 2b.
3. Wind and seismic loading
3.1. Wind load modeling
Wind loading varies both temporally and spatially, and is gen-erally described in stochastic terms. Time-histories of turbulentwind speeds are generated from theoretical or measured powerspectral density (PSD) expressions and coherence functions. Forthis paper, the Kaimal model is used. The form of the Kaimal spec-trum specified in IEC 61400-1 is
fSkðf Þr2
k
¼ 4fLk=Vhub
ð1þ 6fLk=VhubÞ5=3 ð13Þ
where f is the frequency in Hz, Vhub is the wind speed at hub height,k is the index referring to the velocity component direction, Sk is thesingle-sided velocity component spectrum, rk is the velocity com-ponent standard deviation, and Lk is the velocity component inte-gral scale parameter. Coherence, a measure of the similaritybetween time histories at two spatially separated points, is given by
Cohðr; f Þ ¼ exp �12ððfr=VhubÞ2 þ ð0:12r=LcÞ2Þ0:5h i
ð14Þ
where f is the frequency under consideration, r is the spatial sepa-ration between two points, and Lc is the coherence length scale,equal to Lk for the along-wind direction.
A method for computing a set of coherent random wind timehistories is as follows [7]. First, a matrix is created:
Sjk ¼ cohjk
ffiffiffiffiffiffiffiffiffiffiffiSjjSkk
qð15Þ
where cohjk is the coherence in the wind field between points j andk, and Sjj and Skk are the respective PSD functions at points j and k. Alower triangular matrix H is created for each frequency by an iter-ative scheme such that
H11 ¼ S1=211 ð16Þ
H21 ¼ S21=H11 ð17Þ
H22 ¼ ðS22 � H221Þ
1=2 ð18Þ
H31 ¼ S31=H11 ð19Þ
..
.
Hjk ¼ Sjk �Xk�1
l¼1
HjlHkl
!,Hkk
ð20Þ
Hkk ¼ Skk �Xk�1
l¼1
H2kl
!1=2
ð21Þ
The H matrix can be thought of as weighting factors for a set of unitGaussian white noise inputs which will generate a set of output sig-nals with the desired PSD and coherence [19]. A vector V = Vj(fm) isthen created whose components are
where j corresponds to the number of points, m is an index corre-sponding to the frequency component, and ukm is a randomly gen-erated phase angle. Eq. (24) defines the amplitude of the vector, andEq. (25) defines the tangent of the phase of the vector. The time his-tories at the j points can then be computed by adding the fluctuat-ing components to the mean wind speed as
UjðtÞ ¼ U þXN=2
m¼1
2AmpjðfmÞ cosð2pfmt �UjðfmÞÞ ð26Þ
These time histories are applied to the structure at appropriatepoints. The corresponding blade loading is calculated using the liftand drag characteristics of the blade. The wind speeds seen by theblade at a given cross-section are shown in Fig. 3.
Vibration Isolator
Isolator Constraint
Rotational Coupling
(a)
(b)
Fig. 2. (a) Front view of turbine showing location of vibration isolator; (b) finiteelement model showing locations of rotational coupling and isolator constraint.
Fig. 3. Velocity triangle and force diagram for the wind turbine blade.
226 C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234
In Fig. 3, x represents the rotational velocity of the turbine, r isthe distance from the center of the hub to the cross-section, V0 isthe oncoming wind speed, a and a0 are induction factors which
are functions of the blade geometry and wind speed, Vrel is theresultant effective wind speed calculated as the vector sum ofthe along-wind and across-wind velocity components in the figure,u is the angle between the resultant wind speed and the rotorplane, h is the angle between the chord line of the blade and therotor plane, and a is the angle of attack of the effective wind. Theoncoming wind speed, V0, corresponds to the randomly generatedwind speeds Uj in Eq. (26). The forces imparted to the blade are alsoshown in Fig. 3.
In Fig. 3, L and D are the lift and drag forces per unit length,respectively. Forces pN and pT are the axial and tangential forcesper unit length, whose magnitudes are given by
pN ¼ 0:5qairV2relCac ð27Þ
pT ¼ 0:5qairV2relCtc ð28Þ
where qair is the mass density of air, c is the chord length of theblade, and Ca and Ct are the axial and tangential force coefficients,respectively. The force coefficients are calculated as
Ca ¼ CL cos uþ CD sin u ð29Þ
Ct ¼ CL sinu� CD cos u ð30Þ
where CL and CD are the lift and drag coefficients of the blade.Expressions for the axial and tangential force coefficients followfrom resolving the lift and drag force vectors in Fig. 3 into axialand tangential force vectors.
The rotation of the blades about the center of the hub causes atension force which varies along the length of the blade, given by[14]
FtðrÞ ¼Z LþRh
rmðrÞx2dr ð31Þ
where r is the distance from the center of the hub to a point on theblade, m(r) is the linear mass density of the blade at distance r fromthe centre of the hub, x is the rotational speed of the blade, L is thelength of the blade, and Rh is the radius of the hub. The applied ten-sion increases the effective stiffness and natural frequencies of theblade and may significantly affect the structural response underloading which has a broad frequency spectrum.
Wind speed time-histories are created by using the PSD andcoherence functions of Eqs. (13) and (14) as inputs to the schemedescribed in Eqs. (15)–(26). The wind speed time histories are thenconverted to wind force time-histories using Eqs. (27)–(30). In thedynamic structural problem, the velocity of the structure must besubtracted from the oncoming wind speed in order to capture theeffects of aerodynamic damping. This is accomplished by subtract-ing the structural velocity from the oncoming wind velocity shownin Fig. 3.
3.2. Seismic loading
Seismic loading is caused by ground acceleration, with appliedforces proportional to the mass of the structure. For lateral groundmotion,
Fseismicðx; y; zÞ ¼ �mðx; y; zÞ€xg ð32Þ
where Fseismic is the effective applied force due to ground shaking,m(x, y, z) is the mass distribution of the structure, and €xg is theground acceleration.
For seismic loading, three measured ground acceleration timehistories from the 1994 Northridge earthquake are used; thesetime histories were retrieved from the Pacific Earthquake Engi-neering Research Centre’s NGA database. These time histories weremeasured at Newhall County Fire Station (denoted NH), Sylmar
C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234 227
District Converter Station East (denoted SC) and Rinaldi ReceivingStation (denoted RS). The station codes, from the NGA database,are CDMG 24279, DWP 77, and DWP 75, respectively. Each seismicrecord consists of two orthogonal components of ground accelera-tion. Since the current study is concerned only with motion in thealongwind direction, a single component of each ground motion isapplied for each case. The seismic records used are denoted in theNGA database as NWH360, RRS228, and SCE018, respectively. Theyare shown in Fig. 4. The NH, RS and SC time histories havemaximum ground acceleration magnitudes of 0.59g, 0.83g, and0.83g, respectively. The responses are calculated by numericallyintegrating the equations of motion in the time-domain using theRunge–Kutta method in COMSOL.
4. Simulation parameters and response variables
The turbine selected for this study has a hub height of 60 m. Thetower is a linearly tapered cylindrical steel shell with an outerdiameter of 3.8 m at the base, outer diameter of 2.3 m at the top,and a constant thickness of 35 mm. The tower steel has Young’smodulus of 210 GPa and mass density of 7850 kg/m3. The bladesare rectangular box sections having outside dimensions of 3 m by0.8 m at the base tapering linearly to 1.5 m by 0.8 m at the tip, withthe short side oriented in the along-wind direction and the longside normal to the wind. The blades have a shell thickness of15 mm. The blade material has Young’s modulus of 65 GPa andmass density of 2100 kg/m3. The blades are 30 m long with a 3 mhub radius, and have a pitch angle, corresponding to angle h inFig. 3, which varies linearly from 0.2 radians at the base to 0 radi-ans at the tip. The mass of the hub is 20,000 kg, the mass of the
0 5 10 15 2-1
-0.5
0
0.5
1
Tim
Gro
und
acce
lera
tion
(g)
0 2 4 6 8 1-1
-0.5
0
0.5
1
Tim
Gro
und
acce
lera
tion
(g)
0 5 10 15 2-1
-0.5
0
0.5
1
Tim
Gro
und
acce
lera
tion
(g)
Fig. 4. Ground acceleration time histori
nacelle is 50,000 kg, and the offset between the tower and theblades is 5 m.
The relationship between the angle of attack of the wind andthe lift and drag coefficients is chosen based on previously dis-cussed literature. It is assumed that the lift coefficient is definedat a number of angles of attack, as given in Table 1. At intermediateangles of attack, linear interpolation is used. The drag coefficient isassumed to be a continuous sinusoidally varying function of theangle of attack, equal to a minimum of zero at a 0� angle of attackand a maximum of 1.8 at a 90� angle of attack. The induction fac-tors a and a0 are assumed to be zero for computational simplicity.The mass density of air is assumed to be 1.25 kg/m3.
The first 5 natural frequencies of the wind turbine in the parkedposition without the vibration isolator, pertinent to the alongwindmotion, are given in Table 2. The first five natural frequencies rep-resent a total participating mass of 82%, indicating that the massparticipation of the structure is not confined to a few dominantmodes. Structural damping is implemented using the Rayleighform, with the damping coefficients for the tower correspondingto a damping ratio of 1% of critical based on the first two along-wind sway modes of the structure and the damping coefficientsfor the blades corresponding to a damping ratio of 1% of criticalbased on the first two flexural modes of the blades.
The isolator is assumed to be located 2 m below the top of thetower, at a height of 58 m. The vertical extent of the isolator isnot considered. The isolator is implemented such that displace-ments in the x and y directions are coupled. The isolator is rigidin the vertical direction and for rotation about all 3 directionalaxes. The ratio of post-yield stiffness to initial stiffness is 0.1 andthe exponent n is 2. A yield displacement of 50 mm is chosen sothat there is a clear elastic range for the isolator at low
0 25 30 35 40
e (s)
0 12 14 16 18 20
e (s)
0 25 30 35 40
e (s)
es for Newhall, Rinaldi and Sylmar.
Table 1Discrete values of lift coefficient.
Angle of attack (�) Lift coefficient
0 0.010 1.025 0.7540 1.090 0.0
228 C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234
displacements, and to minimize yielding under operational windloading, which has a static component. The isolator stiffness anddamping are varied in the simulation studies. The initial isolatorstiffness ranges from 1500 kN/m to 15,000 kN/m. The initial isola-tor stiffness of 1500 kN/m corresponds to a post-yield isolator nat-ural period of 4.1 s. The damping values range from zero to 20% ofcritical. The equivalent isolator natural period is calculated as thenatural period of the isolator if both the tower and blades were ri-gid, corresponding to a single degree of freedom (SDOF) system.The stiffness of the SDOF system is equal to the isolator stiffness,and the mass of the SDOF system is equal to the total mass locatedabove the isolator. The damping coefficient is calculated based onthe post-yield stiffness to avoid unrealistically high dampingforces.
For seismic analysis, the occurrence of a design earthquake isassumed to be a rare event, and the design seismic loading is unli-kely to coincide with extreme wind loading. A mean wind speed of10 m/s is chosen, with a turbulence intensity of 0.18, as per IEC61400’s Normal Turbulence Model. This wind speed is a represen-tative value for normal operation of the turbine.
Wind speeds are simulated at ten points along the radius of therotor denoted ‘‘1’’ through ‘‘12’’ in Fig. 5. As the blades rotate, thewind speed applied to each blade varies with time; as the bladepasses from one radial line to the next, the corresponding wind
Table 2Natural frequencies and modes of the turbine.
Mode 1 Mode 2
Mode 3 Mode 4
Mode f (Hz)
1 0.57
2 1.41
3 1.54
4 3.61
5 4.20
Mode 5
speed time history is applied. The effect of time-varying forceson the structure is simulated using the rotational coupling equa-tions presented in Eqs. (2)–(6). In order to minimize the transientsassociated with a suddenly applied force, the time histories arepre-processed by having the mean wind speed increase linearlyfrom zero at time zero to its full value of 10 m/s at 10 s, remainingat the full value after 10 s. The PSD function described previously isused at all points. The time histories applied to the tower aremultiplied by a power-law profile in order to provide a more real-istic wind profile close to the ground. A grid of 40 s time historiesare simulated at the points previously described, as well as at tenpoints along the height of the tower. These time histories have asampling rate of 20 Hz. A typical wind speed time history is shownin Fig. 6.
The effectiveness of vibration isolation is quantified by compar-ing the response of the isolated turbine to that of the un-isolatedturbine. For this study the primary response quantities of interestare structural actions: base shears and bending moments in thetower and blades, structural displacements and structural acceler-ations. For strength design, it is important to study the peak valuesof the response. As well, it is useful to know the standard deviationof the response for evaluating concerns such as reliability, avail-ability, and fatigue life.
The key response variables considered for the isolated turbinestructure are denoted by J1–J8 where: (a) J1 is the hub displace-ment relative to the ground, (b) J2 is the hub acceleration, (c) J3is the tower base shear, (d) J4 is the base tower base bending mo-ment, (e) J5 is the maximum blade base shear, (f) J6 is the maxi-mum blade base bending moment, (g) J7 is the displacementacross the isolator and (h) J8 is the force transferred across the iso-lator, including the damping force. Quantities (a)–(f) are normal-ized with respect to their un-isolated counterparts, while (g) and(h) are normalized with respect to their values at yield. Addition-ally, the following three objective functions are used:
O1 ¼ kinematic objective function ¼ J21 þ J2
2
2ð33Þ
O2 ¼ tower response objective function ¼ J23 þ J2
4
2ð34Þ
O3 ¼ blade response objective function ¼ J25 þ J2
6
2ð35Þ
The isolator properties which minimize a given objective func-tion can be considered to be the optimal parameters with respectto the corresponding response variables. The objective functionswere selected such that if both of the response parameters consid-ered were equal to 1, indicating no change in structural response,the objective function would also be equal to 1.
The theoretical descriptions of wind turbine structures, loadingand vibration isolation in the preceding sections are implementedusing MATLAB and COMSOL Multiphysics. MATLAB is a technicalcomputing program, and is used mainly for simulation of windloads and post-processing, while COMSOL is a finite element suiteand is used to solve the differential equations of motion to studythe behavior of the turbine. The vibration isolator is implementedin COMSOL by adding the differential equations for the hystereticdisplacement as global equations to be solved alongside the equa-tions of motion. The hysteretic displacements are solved simulta-neously with the equations of motion and are used in globalequations to calculate the forces applied by the isolator. Theseforces are applied to the structure at the nodes corresponding tothe top and bottom of the isolator. The blades, nacelle and towerare modeled using 3-dimensional frame elements, with the nacelleelements having structural properties such that they are effectivelyrigid. The masses of the hub and nacelle are lumped at the base ofthe blades and the top of the tower, respectively. The base of the
1
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Fig. 5. Locations of wind simulation points showing blade rotation.
0 5 10 15 20 25 30 35 400
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Time (s)
Win
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eed
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Fig. 6. Sample synthetic wind time history.
C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234 229
tower is specified as a fixed support. The tower and blades are eachseparated into 10 frame elements having varied structural proper-ties and loading, in order to capture the effects of varied structuralgeometry and turbulent wind loading.
The rotational coupling between the blade–hub system andthe nacelle is accomplished by defining a time-dependent rotat-ing coordinate system. The displacements and rotations at thetip of the nacelle are constrained to be equal to those at the baseof the blades, appropriately transformed by the rotating coordi-nate system, as in Eqs. (2)–(6). The effects of centrifugal stiffeningare incorporated using an approximate method in which thefundamental frequency of a rotating blade is calculated usingMATLAB and a multiplier proportional to the centrifugal tensionis applied to the elastic modulus of the blades in the finiteelement model to match that natural frequency. Turbulent windspeeds are simulated in MATLAB using the method described inEqs. (15)–(26). The calculated wind speeds are input into COMSOLas functions. COMSOL allows for the calculation of distinct localproperties for each frame element. Each frame element isassigned a numeric index to identify which wind speed time his-tory is applied to it. The structural and aerodynamic propertiesdescribed by Eqs. (27)–(30) are calculated for each blade segment,and then used to determine the along-wind and tangential load-ing on that segment. The loads calculated for both the tower andblades are then applied to the structure. Records of seismicground acceleration are also input into COMSOL as functions.The ground accelerations are multiplied by the mass of the struc-ture and applied as loads to the frame members as well as thelumped masses at the hub and nacelle.
COMSOL’s implicit backward interpolation solver [4] is used forall simulations, with a time-step of 0.001 s, selected to provide
accuracy and stability for direct solution of the equations ofmotion.
5. Simulation results and discussion
5.1. Seismic loading
The simulation regime consists of two studies, the first to inves-tigate the effect of the vibration isolator under seismic loading andthe second to investigate its effect under combined seismic andwind loading. Prior to evaluating the response for the isolated case,simulations were performed to determine the baseline structuralresponse of the un-isolated turbine. For the seismic study, the re-sponse of the isolated turbine is evaluated under a range of isolatorstiffness and damping values. The isolator stiffness variation is ex-pressed by the non-dimensional quantity, frequency ratio, which isthe ratio of the pre-yield isolator circular natural frequency (com-puted using the initial isolator stiffness and the mass above the iso-lation level) to the first circular natural frequency of the un-isolated structure. The damping is varied between 0% and 20% crit-ical (based on post-yield stiffness of the isolator) for all the seismiccases. The results of the simulations for Newhall, Sylmar and Rinal-di earthquakes in terms of the performance indices J1–J6 areshown in Figs. 7–9. The peak isolator response quantities (J7 andJ8) are shown in Figs. 10–12. The performance indices (J1–J8) aretabulated for three frequency ratios (2.0, 2.6 and 3.1) and three iso-lator-damping ratios (0%, 10% and 20%) in Table 3. A sample time-history illustrating the hysteretic behavior of the isolation systemfor the case of Newhall earthquake is shown in Fig. 13. This study(earthquake case only) is performed with the turbine in the parkedposition with one blade vertical.
From the results, it is observed that the hub displacement of thestructure is decreased by the isolator, with a minimum valueoccurring at a frequency ratio of 2.0 under Newhall and Rinaldiexcitations, and at a frequency ratio of 2.3 under Sylmar excitation.The hub acceleration does not show a minimum, but shows a gen-eral trend of increasing as the isolator stiffness increases. Both thehub displacement and acceleration show decreases or very modestincreases across the range of isolator stiffness. The tower baseshear shows a decrease at frequency ratios above 1.6, minimumvalues at a frequency ratio of 3.1 for Newhall and Rinaldi excita-tions, and a relative maximum at the same frequency ratio forthe Sylmar excitation. For all three excitations the tower base shearis generally reduced by the presence of the vibration isolator. Thetower base moment shows a decrease at frequency ratios below3.3 for all three excitations, with a general trend of increasingtower base moment with increasing frequency ratio. The bladebase shear and blade base moment show decreases or very modestincreases at frequency ratios above 1.6. Both variables show mini-mum values between frequency ratios of 2.1–3.1, suggesting anoptimal stiffness value in that region.
At low values of isolator stiffness, the peak values of the isolatordisplacement are very large, indicating that the isolator displaces farpast its linear elastic range. For the frequency ratio range of approx-imately 2.1–3.1, the normalized isolator displacement ranges fromapproximately 3 to 6, corresponding to a peak isolator displacementbetween 150 mm and 300 mm. This displacement, while relativelylarge, can reasonably be accommodated by a properly designed iso-lation system. In the same range of frequency ratios, the normalizedisolator force varies from approximately 1.2 to 2.
The effect of increasing the isolator damping depends on theparameter in question as well as the seismic event under consider-ation. Generally, the effect of increasing the viscous damping coef-ficient is not significant for the peak hub displacement and peakhub acceleration. The effect of increasing the viscous damping is
12
34
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Frequency RatioDamping Ratio
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emen
t
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er B
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ase
Shea
r
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34
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Bla
de B
ase
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ent
Fig. 7. Simulation results for the case of Newhall earthquake.
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er B
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er B
ase
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ent
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ase
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r
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Frequency RatioDamping Ratio
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de B
ase
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ent
Fig. 8. Simulation results for the case of Sylmar earthquake.
230 C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234
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ase
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Fig. 9. Simulation results for the case of Rinaldi earthquake.
1 1.5 2 2.5 3 3.5 4 00.05
0.10.15
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ator
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Damping RatioFrequency Ratio
Isol
ator
For
ce
Fig. 10. Peak isolator performance indices for Newhall earthquake.
1 1.5 2 2.5 3 3.5 4 00.05
0.10.15
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Damping RatioFrequency Ratio
Isol
ator
Dis
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t
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2
3
4
Damping RatioFrequency Ratio
Isol
ator
For
ce
Fig. 11. Peak isolator performance indices for Sylmar earthquake.
C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234 231
more pronounced for the case of tower base shear, and is depen-dent on the earthquake under consideration and the frequency ra-tio. Overall, the effect of increasing the damping ratio is to reducethe tower base shear. The effect of damping on the base moment,blade shear and blade moment does not appear to be significant,
for the range of damping ratios considered. The effect of viscousdamping in the isolation layer is most evident in reducing the dis-placement across the isolator. This quantity (J7) reduces withincreasing isolation damping, while the isolator force remains rel-atively insensitive to the increase in the damping.
1 1.5 2 2.5 3 3.5 4 00.05
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ator
Dis
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ator
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ce
Fig. 12. Peak isolator performance indices for Rinaldi earthquake.
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3-600
-400
-200
0
200
400
600
Isolator Displacement (m)
Isol
ator
For
ce (
kN)
No Damping10% Damping20% Damping
Fig. 13. Typical force–displacement plot for Newhall seismic excitation withfrequency ratio of 2.60 with varied damping.
232 C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234
In order to better quantify the observed minimum values, theobjective functions previously defined for kinematic response,tower response, and blade response are plotted against the fre-quency ratio. The objective functions for a fixed value of 10% isola-tor damping are shown in Fig. 14. The objective function for bladeresponse shows a minimum at frequency ratios between approxi-mately 2.1 and 3.1. The objective functions for the kinematic andtower responses do not show clear minimum values, but their
Table 3Performance indices for the seismic cases.
Key response variable EQ. Frequency ratio2.0Isolator damping ratio (%)
numerical values show that the associated normalized parametersare decreased in the range of the minimum value for the blade re-sponse objective function.
Based on the results, a frequency ratio between 2.1 and 3.1 pro-vides significant reductions in all key response variables under thethree seismic loading cases.
5.2. Wind-only and combined wind and seismic loading
For this case, the un-isolated and isolated turbine structures areeach subjected to a set of coherent wind speed time histories, inaddition to the seismic loading. The isolated turbine structurehas an isolator yield displacement of 50 mm. Simulations are per-formed for a frequency ratio of 2.6 with an assumed damping ratioof 10% based on the post-yield stiffness. The performance indices(both peak and standard deviation) for earthquake (turbine in
Frequency ratio Frequency ratio2.6 3.1Isolator damping ratio (%) Isolator damping ratio (%)
C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234 233
the parked condition), wind-only and combined wind and seismicloading are tabulated in Table 4. These values are presented both interms of their normalized performance indices as well as in theirabsolute units for comparison. For the sake of brevity, only onecase of Newhall earthquake for a single frequency and damping ra-tio (2.60 and 10%) is presented. The trends are expected to be thesame for other frequency and damping ratios of interest in thisstudy.
From the results (in Table 4), it is not surprising that the hubdisplacement for the wind-only case is increased compared tothe un-isolated case. For this case, the peak hub displacement ofthe turbine is greatly increased for low values of frequency ratio,while the other parameters are generally decreased (results forother frequency ratios are not shown due to space limitations).The magnitudes of the peak hub acceleration, tower base shearand moment, and blade base shear and moment, all show de-creases in response. The decreases in response are not stronglydependent on the frequency ratio, as it was observed that the per-formance indices are relatively constant for the range of frequencyratios studied here. The magnitudes of the decrease in peak re-sponse are typically less than 10% for the shear and moment inthe blades and tower. The standard deviations of the key responsevariables are significantly decreased, by more than 50% for both theshear and moment in the blades and tower. This result demon-strates that implementing a vibration isolator to mitigate the effectof seismic loading can also mitigate the effect of wind loading. Thevariation of structural response is decreased by the use of vibrationisolation, which may be useful in designing the turbine againstmaterial fatigue. For the range of stiffness ratios considered forseismic loading, the reduction in the structural response underwind loading is relatively constant.
For the combined wind and seismic case, the hub displacementand isolator displacement are greater than the sum of the individ-ual seismic and wind cases. The hub acceleration, and base shearsand moments are less than the sum of the cases. This is likely duepartially to the nonlinear nature of the isolation system and alsopartially because for the seismic case the blades are stationary,so the shears and moments, particularly in the blade that is verti-cal, are larger than they would be with blade rotation.
It is desirable for the isolator to yield only in extreme loadingevents such as earthquakes. Under the operational-level wind loadconsidered here, yielding of the isolator may necessitate frequentre-centering, and an isolator stiffness low enough to allow yieldingunder operational wind loading would undergo excessive displace-ments under extreme wind and seismic events. These excessivedisplacements could pose a problem when designing the isolatorfor strength and stability. For operational wind loading, in general,higher isolator stiffness is desirable. For structural design of a tur-bine, more detailed wind loading would be considered, includingdeterministic gusts and direction changes, and extreme turbulenceand wind speeds. It may be difficult to design a passive isolationsystem as described which yields in seismic events but remainsin the linear elastic range for all wind loading events. In that case,a system could be designed where the isolator would yield in cer-tain extreme wind events as well. Alternatively, a more sophisti-cated system which includes a structural fuse could beinvestigated, but is considered beyond the scope of the presentstudy.
6. Conclusions
The values of the key response variables indicate that vibrationisolation is a feasible solution for reducing the structural responseof a wind turbine under wind and seismic loading. Detailed designand implementation of vibration isolation could allow wind
234 C. Van der Woude, S. Narasimhan / Engineering Structures 60 (2014) 223–234
turbines to be deployed in seismically active areas without theneed for costly strengthening and redesign to resist seismic load-ing. The isolation system could also decrease response under windloading, allowing for more efficient use of material and/or in-creased fatigue life.
In the range of frequency ratios considered here, nearly all ofthe key response parameters are decreased relative to the un-iso-lated turbine. Under seismic loading, changing the degree of damp-ing associated with the isolator does not have a monotonicallydecreasing effect on the structural response of the turbine aswould be expected in an un-isolated structure. Modifying dampingincreases some key response parameters and decreases others,depending on the damping level and the loading scenario consid-ered. The results of this study demonstrate that detailed consider-ation of vibration isolation systems for wind turbines may lead tosignificant increases in structural capacity, reliability and econ-omy. The large displacements which might occur in the isolationlayer during earthquakes can be mitigated through the use of ac-tive or semiactive vibration dampening systems, and this is anexciting area for future research. The added versatility of isolatedwind turbines could contribute to the continued growth of thewind energy industry worldwide. In the future, a more comprehen-sive seismic hazard and vulnerability analysis needs to be under-taken to study the effects of partial isolation for a range ofturbines and risk scenarios. The effects of bi-directional couplingfor two directions of ground motions also need to be investigated.
Acknowledgement
Funding for the research contained in this paper was providedby the National Science and Engineering Research Council ofCanada, and is gratefully acknowledged.
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