Vibration Measurements

7/29/2019 Vibration Measurements

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~ Bruel & Kjr


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IntroductionThis booklet gives an introduction to the methods usedin vibration testing and a description GI tne vibrationexciters and control equipment used in environmental1estlng and in determlna,tlmll of dynamic proper\Jies ofstructures.

IntroductionWhy vibration lesting?How does an exclter work?The power amplifierThe exciter controlBasic exciter Instrumentation,Sine excitationRandom excitationEnvironmental teatingMounting of the teat objectFixturesStatic compensationVibration ,reaponae linveatigationEndura,nce conditioningSwept sine testingConditioning at aingle frequenciesRandom teatingDerivation of teat dataStructural, rHearchMecl1anlcal impedance and mobilityAddJtion of impedances and mobllltiesComplex elastic modulusMode studiesResonance studleaUse 0' complex plotsExcitation methodsMulti-shaker syatfitfl1s

1983

See paQe123445567789101111121314151617181920212223


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Why Vibration Testing?Due to the demands of high speed operation and the useof light structures In modern machinery, static measure-ments of stress/strain properties are not sufficient . Dy-namic measurements are necessary and vibration 'test-ing has therefore found widespread use.In the environmental laboratory, vibration testing is performed as part of a company's quality assurance pro-gramme together with for example temperature and hu-midity tests to ensure product reliability. The test objectis exposed to a certain vibration level according to aprocedure specified by national and Internatronaistandards,To find the dynamic properties of a structure, the re-sponse to a vibrational force Is of interest rather than theactual vibration level. This concept is found for instancein determination of the ability to transmit or damp vibra-tions or In the description of the vibrational modes of astructure at resonances.In the calibration of vibration transducers a comparisonis made between the transducer to be calibrated and areference transducer at a prescribed vibration level.To produce a defined vibration an electromagnetic vi -bration exciter (also called a shaker) Is used. This con-verts an electric signal Into a mechanical movement,controlled to maintain a certain vibration level or force.

Environmental TestingCalibration


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How Does an Exciter Work?In principle the electromagnetic vibration exciter oper-ates like a loudspeaker, where the movement is pro-duced by a current passing through a coli in a magneticfield. The force used to accelerate the moving element isproportional to the drive current and the magnetic flux .Therefore by controlling the current, the vibration levelof the exciter can be controlled.In small exciters the magnetic field is produced by apermanent magnet, whereas in the larger ones electro-magnets are necessary. The maximum current and theload determines the acceleration level which can be ob-tained. At low frequencies, however, this accelerationlevel will decrease due to displacement limitations of themoving element. Resonances in the moving element willset the upper frequency limit.The performance of an exciter is presented in a diagram,sh.owing the maximum acceleration as a function of fre-quency. With double logarithmic scales the displacementlimit will be represented by a straight line with a slope of12 dB/octave. A velocity limit is often also found, espe-cially with the larger exciters, and this is Indicated by aline with a slope of 6 dB/octave.

Flexure

DrivecoilF=BIL

F=ma

E:s..CS....!!QI(.)(.)cs

~

t F Exciter table

IF = force IN ]B = 17Ulgn.etic flux intensity IT }I = current lA]L = length Im ]m = mass {kg]a = acceleration Im/s2]

fflO "tlm, r2ff lalog frequency

fI20501 3


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The Power AmplifierThe frequency response fo r an exciter driven by a con-stant current will show three regions of different na-ture. The first two regions represent the spring-masssystem of the moving element and Its suspension witha resonance of typically 20 Hz. In the third region, typi-cally above 5 kHz for big exciters, axial resonances inthe moving element will occur, set1lng the upper opera-tional frequency of the exciter.A response curve for an exciter with a constant voltageinput will show the same regions of control, but the lowerresonance is considerably damped, giving an easiercontrol of the level. The voltage control, obtained by itlow Impedance amplifier is normally preferred. In somecases, however, a current control will be advantageous,primarily when the exciter is used as a force generatoror where non-feedback control is required using the midfrequency range of the e)(citer. This demands a highimpedance output and therefore amplifiers will oftenhave selectable impedance outputs.

The EXCiter ControlThe use of a vibration exciter assumes a constant vibra-tion level at the table. The frequency response curve isnot flat. it contains resonances, and other resonanceswill be introduced when a test object Is mounted on theexciter. When used throughout a frequency range thegain of the amplifier must consequently vary with fre-quency. This gain is set by a controller, receiving feed-back information from the test object. The main ele-ments of an exciter control must therefore be a frequen-cy generator, a vibration meter and a level contrOlling

-4 circuit.

IIConstant Current

i.-prinJl:f. ..... ..o'.0--__ MQ88, controlled eontroUed

Exciter

Amplifier

Resultingacceleration

requeney_


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Basic Exciter InstrumentationA basic set-up consists of an exciter, a power amplifier,an exciter control , an accelerometer or force transducerand a conditioning amplifier.The exciter is selected primarily according to the forceor acceleration requ ired, but other parameters may beimportant such as Its abiUty to take up side loads, thetransverse vibration and the distortion of the waveform.The exciter Is Isolated from its base by springs, in mostcases giving sufficient protection from environmentalvibration when bolted directly on the floor. However, toreduce the vibration transmitted to the building by excit-ers used for high level applications, the exciter must bemounted on resilient material or a seismic block.

Sine ExcitationSine signals, swept or at a single frequency, are by farthe most commonly used excitation Inputs: the control isrelatively simple, a large amount of reference materialexists, and the response Signals are easy to measure.When the signals are swept, a feedback control, knownas a compressor Is applied. The demand to the com-pressor is that it shOUld be fast enough to react to lowdamped resonances even at high sweep rates. A dynam-ic range of at least 80 dB and compressor rates up to1000 dB/sec are normally found.Sine signals are described by their frequency and ampli-tude. In Vibration testing the amplitude is normally Interms of peak values (displacement 8S peak-peak) withfrequencies ranging between 2 and 10,000 Hz.

, . . - - - - - - - - - - - - - . ~ .-.--.,,,i ' r"----,III: tL -__ -- 'IIIIIIII

Specified level

______ .0._ - - _ __ ~Ji'requenC)l

5


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Random ExcitationA random signal used in vibration testing has a continu-ous spectrum, with amplitudes varying according to aGaussian distribUtion. Within the specified frequencyrange any ampJlludes should be present, but in practicethe generators and amplifiers will give limitations. Invibration testing It is generally demanded that a randomSignal should contain peak-values of three times theRMS value.The force produced by an exciter is mainly limited by theheating effect of the cur rent. i.e. the RMS value. whereasthe power amplifier rating is influenced by the peakvalues. To give the same force the amplifier must there-fore be larger when used with random than with sineexcitation.The random spectrum is described by its power spec-tral density or acceleration spectral density. ASDm/s2)2/HZJ. To shape and control this. the vibrationmust be analyzed by a narrow band analyzer and com-pressor loops applied to ea9h bandwidth. Digital tech-niques based on Fourler transforms are normally usedand the control is achieved using a computer, a pro-cess called equalization.The random capacity of an exciter is specified as themaximum acceleration spectral density at differentloads of a spectrum, shaped according to the Interna-lional Standard, ISO 5344.

P_k = {2RMS

I(1bl :1000

( 1'00 ye. 0. 0test spectrumtJcoording toISO 5344

.-2000 freqlUncy. Hz7


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Environmentall TestilngAn environmental test Is performed to determine theability of equipment to withstand specified severltles ofvibration, shock, temperature, humidity, etc. The re-quirements may be set by the user or the supplier withreference to some national or military standard. Thesestandards describe the test procedures, but do not statethe individual test levels.The fundamental standards are IEC 68, tests Fc and Fd,which in several countries have been accepted as na-tional standards. The contents of all standards largelyfall Into 3 groups: the mounting of the test object, theendurance conditioning and the vibration responseinvestigation.

Mounting of the Test ObjectAs the test Is performed to simulate the environmentalinfluence, the object must be mounted on the excitertable by its normal means of attachment. In most casesthis requires a speCial fixture, which allows the specimento be vibrated along the specified axes.The method of mounting must be described in the test,and so must the point on the specimen to which thecontrol accelerometer is attached. Also, It must be spec-ified whether the object should be operating during thetest.

TEST STANDARDS-Mounting the specimen- Vibration response investigation-Endurance conditioning

- 7

~ = = ~ -


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- - -

8

In cases where the test object cannot be mounted dIrect-lyon the exciter tab le a fixture, sometimes Of a rathercomplex nature. is required for fastening the object. Thefixture must be stiff enough to transmit the generatedforce or motion uniformly to the test object. thus notIntroducing any resonances. It is important to check thedesIgn by measuring the vibration levels on the surfaceof the fixtures by means of accelerometers. All reso-nances must tie outside the test frequency range.The natural frequency of a construction will be almostthe same whether the material is steel or aluminium andas the total weight of test object and fixture is a restrIct-Ing tactor in the application of an exciter. aluminium willnormally be the best choice.To obtain a high resonance frequency. it wilt always benecessary to over-dimension the structure, so no con -siderations normally have to be taken concerning themechanical strength.For minimizing the weight of the fixture it can be con-structed of relatively thin plates, supported by braces.The plates are of Simple geometric shapes with respons-es easy to calcu late . Much care should be taken In as-sembling: bolts can introduce spring/mass effects, weld-Ing can introduce Internal stresses.If resonances cannot be avoided the damping can beIncreased by laminating with a damping material such asrubber or by filling cavities with foamed plastic.


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Static CompensationHeavy test objects will cause a static deflection of the

~ x c l t e r table dependent on the stlHness of the flexures.This decreases the available displacement for the dy-namic performance and It may be necessary to com-pensate for this stattc loading when operating withlarge dynamic dlsplacements, i.e. especially In the lowfrequency range. A simple means of compensating Isto apply a DC current to the moving call, but as thiscurrent contributes to the heating of the ex.citer andpower amplifier, the dynamic performance will be re-duced. The compensation is therefore more oftenmade by ex.terIi1S:! mechanical supports, e.g. springssuspended from tlile ceiling. horizor'ltal slip tables sup-ported by flexures, or sliding on an 011 film.

tDC-Currentr -----------, . - - ----1\---"'--7\ ---___________I ..-----.[------=J----_____ 'V. __')J__\l

t- Mcrc#uJnical Stop


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Vibiratlion ResponseInves'tig1ationThe first step atter mounting, the test object is to make avibration response Investigation wl ,h the pl!Jrpose ofchecking its function and to examine the Influence of'resonances throughout the frequency range. For alltypes of tests the resonances are found by a sine sweep.The resonance frequencies are measured and the be-naviour of the structure studied In detail by manuallycontrolling the frequency. At the end of the test proce-dure a slmifar Investigation Is car,rled ou, forcomparison.The behaviour of the structure is most easily studied bymeans of a stroboscopic lamp, triggered by the excitercontrol to follow the excitation frequency. Better, howev-er, is to use a trigger signal which differs slightly fromthe excitation frequency. giving a slow-motion like ,m-age. This slow-motion frequency, normally 3 - 5 Hz, canbe set on the stroboscope to follow the excitation. A-urther study of the behaviour can be made by ms'nuallydelaying the trigger signal to move the Image throughone or more cycles or by using dual flashes to give apicture of the extreme positions of the resonating part.

_ . s.. , ., .I) . . . (;s . ~o 0 ll:...=J 0 0~ ....

~ i i le] t - - -- . . . l: a.:


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Endurance CondiitionilngDuring the endurance conditioning the specimen Issubjected to a vibration, which in severity, I.e. frequen-cy range, level and time, should ensure that It can sur-vive in the real environment. Dependent on these, theconditioning Is performed by sine sweeping, sine test-Ing at the resonance frequencies or at other pre-deter-mined frequenoles, or by random vibration.Swept Sine TestingIn the swept sine test the signal to the exciter Is continu-ously swept back and forth over the appropriate fre-quency range. The main control parameter is the accel-eration level, but below a certain frequency (the cross-over pOint) a constant displacement is chosen. In thelEe-test the cross-over frequency is 60 Hz and the levelsof displacement and acceleration are chosen to changecontinuously from one parameter to another. Other stan-dards, e.g. the military standards, may demand furtherchanges of level or of vibration parameter.Therefore, the eXCiter control used for environmentalsine testing, has at least two measuring channels withintegrators to calculate the displacement and velocitylevels from the acceleration level measured by the con-trol accelerometer. There must also be a switching facili -ty, to change the measuring channel at the cross-overfrequency.

Constant acceleration

IEC swept sinusoidal test

__ Constantacceleration

~ - ; - ~ C r 0 8 s - o v e rfrequencies

t)lpical MIL-testlOll frequenC)!

11


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Conditioning at SinglleFrequenc.iesIf the expected environment is dominated by one or afew discrete frequencies, the endurance cond itioning ismost realistically performed only at these frequencies,often as fatigue testing to break-down of the material.Specimens showing some clearly evident resonancescan successfully be tested at these resonances. Due tochanges in the structure during the test, the resonancefrequency Is likely to move and in order to change ttleexcitation frequency automatically, a resonance dwellunit is used. It works on the fact that at resonance thephase angle between the excitation and the respons.esignals will change drastically. It Is therefore possib le toconsider the phase angle as character istic of the reso-nance, and It is measured and used as a reference in Cl!servo loop contrOlling the excitation frequency.

Amplitude Phase

Frequency Frequency

ForeeResponse _ew Resonance_._ 0 Dwell Unit

Phase Meter _. E51 . r:::=;:')o 0 J..:S..:.:J 0 0@

GeneratorExciter

AmplifierlI


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Random TestingAlthough sine testing is by far the most widely used vi -bration test due to the relatively low price and simpleInstrumentation. a random excitation will better simulatethe real envlronyYlent. In sine testing only a single reso-nance will be excited at a , ime and any mutual influenceof resonances will not be detected. Another advantageof the random testing Is that the time 01 endurance Isshorter because It acts on all resonances at the sametime.A random test Is specified by its acceleration spectraldensity spectrum (ASO), which is shaped by an equaliz-er and controlled by the total acceleration AMS level ofthe spectrum.The high pr ice and complexity is an obstacle 'o r thewider use of random test systems and compromises us-ing excitation without automatic equalization, e.g. by re-cording a computed spectrum on a tape, are met whenthe demands to the reproducibility are small.One approach combining a Simple feed-back controlwith many of the advantages 0' the random spectrum Isthe swept narrow band technique. In a standard sinecontrol the single frequency signal is substituted by arandom band and the overall vibration level is controlledby the compressor. With a fairly narrow bandwidth thecontrol Is satisfactory even fo r low damped resonances.

lD(l ASD

.jj

total rms: :t 1dB31iB

- - - - - ~ ~ ....-- .- - - ........

lEe rondom test, reproducibility high

yOO 11111 Doe)FrequenC31

Swept Random Test


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De'rivation of Test DataThe purpose Of test standards is to ensure that tests a'reperformed in a reproducible way. A range of recom-mended test levels are stated, but not for specific ob-Jects and therefore the severities chosen must be basedon the experience of ttle manufacturer or buyer.

In any case the basis of a test specification is a knowl-edge of the e)(pected environment. This can be obtainedfrom long-time measurements of the vibration levels onsite, normally using portable equipment including an In-strume'ntation tape recorder. The data Is analyzed andan "envelope" of all measured data gives useful informa-tion to the demands of the test.

Frequency

14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _. . . . . . . . . . . . . . . . . . . .i


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Structurall R.esearchCharacteristic to the study of the influence of vibrationson structures is that It involves measurement of theresponse to an applied force. The frequency response isgenerally often called the mechanical impedance, butstr ictly speaking this is confined to be the complex ratioof force to velocity. Other ratios involving force and thevibration parameters, acceleration, velocity and dis-placement are shown in the table.Although the spectra of any of -the parameters will givethe same information, the velocity will generally be uS,edto describe the vibration as experience shows It pre-sents the most " f l a t curve, thus giving a larger dynamicrange. Also, the velocity Is the parameter most closelyrelated to the strain levels in the structure. Therefore themechanical Impedance and the mobility are more com-monly used than the otliler parameters.One example where the mobility has to be consideredIs when vibration measurements on machines are per-formed In order to obtain Information on the stressesappearing inside the machine. The forces cannot bemeasured directly but only through their vibrational re-sponse on bearings etc. This response Is dependent onthe mobility (or Impedance) of the structures andchanges In the mobility spectrum, from f,or example re-pairs, will therefore change tl:1e measured response.

" " F i ' - o r - c - e - - " ~ : I _______ .!Ivibration ~l)ynamic F a- Acceluance -mCl88 a FMe,CMnit$/ F VimpechJnce - Mobility -v F

F dStiffTU!88 - Compliance -d F

15


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Mlechanrcal. Impedanceand MlobilUtyThe mobility spect.rum can be found from a sine sweepwith a constant force applied to the structure by a vibra-tion exciter. The force is transferred via a push rod andmaintained constant by instrumentatfon similar to thatused in environmental testing except that the level ismeasured by a force transducer. The response is mea-sured with an accelerometer and piotted on a recorder,synchronised to the generator frequency.Similarly the Impedance spectrum can be found by main-taining a constant velocity and measuring the force.In most applications only the behaviour at resonances isof interest and as the force here needs only compensatethe internal damping, relatively small exciters can beused even for large structures. On light structures themass of the accelerometer should be low to minimize theinfluence of the additional mass on the dynamic behav-iour of the structure.Often a plot of impedance or mobility as a function offrequency will give sufficient Information, whilst in othercases a further analysis of the response will be neces-sary to give a complete picture of the dynamicproperties.In any case, to understand the curves it may be useful toconsider the structure as consisting of a number ofmasses, springs and dampers, tor which the mechanicalImpedances are easy to calculate.

m

1TUl88 =m/kg]F =n u l = jwm)v

Z=jwm

Mech4nical Impedance. Z

PowerAmplifier

&cciterControl

LevelRecorder

ftiffness = k /NIm] damping = c /N8JmJF=kx= ( J : ) F=cvZ = ~ Z= c]w ~


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Addition of Impedancesand MobilirtiesThe Impedance of the single elements of a s,ructwrewill, on double logarithmic curves, appear as straightlines, and from the single element curves the imped-ance (or mobility) curves for complex systems can befound. The figure to the right shows a simple spring-mass system without damping with, the force acting i r:llparallel. The total impedance of the parallel system Isthe vector sum of the two single ,Impedances, andl theImpedance curve can be constructed as shown. In aseries system however the mobllltles must be added togive the total mobility. The figure below iIIl!Jstrates acombined parallel and series system and its mechani'-cal impedance as a function of freqlJency. The imped-ance and mobility plots not only give informatIon onthe resonance frequencies, but the behaviour (spring-like, mass-like) also gives the designer valuable infor-mation concerning possible modifications.

j ,1jF r e ~ n C ) l ~

Impedance Plots

Z MtUls

F = ma = ( j _ )vF

Z DamJHr

Z= c

F= cv

c::)Z

!=:)

I

&_N

Z " , p . rZ.,.,lfIIIZ Spring

I F = 1 c : c = ~ vj{J)

~

_. 17


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Compl,ex Elastic IModulusThe Modulus of Elasticity, E, of a structure Is defined as1he ratio of the stress, tT, to strain, I . A static determlnation of the modulus does not take into account ttileInternal damping, which results In the stress and strainnot being in phase under vlbratl'on conditions. Wherethe internal damping Is to be considered e.g In plastics,asphalt, concrete and other vlscoelastlc materials, theComplex Modulus of Elasticity must be measured.The Modulus is the vector,al sum of the Elastic alild theDamping Modulus. It Is related to the Loss Factor, 1'/, ofthe material, T} being the tangent of the phase alTlgle, 1/>,between the Elastic and the Complex Modulus.A dynamic test will tIiIel"efore consist of an excitationwith a constant force and measurement of correspond-Ing values of displacement and phase.The figure shows one method with simplified formula fOra beam excited by a sinusoidal force at Its mid-point'.The formula Includes correction factors for compensat-Ing the effects of, mountilTlg ttle probe, transducers etc.

.At low freqlUncietl

E-:E+jE-

{ e -=EO+ f ' I J, ,= tan0

FE=K - c o t l 0:c

: t a n "


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Mode StudiesThe measurement of mobility or mechanical Impedancegives the frequency response function between the pointof excitation and another point on the structure.However, frequency response functions exist betweenall points of the structure, and if the structure Is to bedescribed in this way, the result will be a very largenumber of functions. Data reduction Is therefore neces-sary and the technique used is to describe the modes ofthe structure.At particular frequencies, the natural frequencies, thes tructure will vibrate In a shape called the mode shape.These frequencies are recognized as resonances of thestructure and are indicated as minima on the mechani-cal Impedances curves and maxima on the mobilitycurves.

Resonance FrequencyDampingMode Shape


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Resonance StudiesCharacteristic to the behaviour of a structure at reso-nance is the increase of vibration amplitude and thechange of phase between force and response. Higherdamping gives a lower and broader peak and a phasechange over a broader frequency range. The damping isdescribed by the quality factor a, related to the band-width of the response curve at the half power points(3 dB from the maximum amplitude).An amplitude and a phase curve will give adequate infor-mation of well separated resonances, but for curves withresonance peaks strongly overlapping, the informationis difficult to Interpret.Plotting the response in a vectorial diagram, a Nyquistdiagram has proved to be more convenient. The axes Ina Nyqulst diagram are the real and imaginary parts of theresponse. The numerical value of the vector is equal tothe amplitude and the angle to the real axis equals thephase angle between the excitation and the response.Thus each point on the periphery corresponds to a cer-tain frequency.A resonance will be represented by a circle, where theintersection with an axis takes place at the resonancefrequency, the axis dependent on the phase-relationshipbetween force and response. The size of the circle de-pends on the damping. a higher damping giving a small-er circle.Instead of being plotted against each other the realand Imaginary part of the response can also be ploltedagainst frequency.

M

1".

Q - ~- /.-'1

,M(/)::..1tC... .L.:.--. . ,L.-II_. . .R.I",

M,..

01 .

F

Iq~ - - - -I: tI ' I II , .AI , II ' 1I II I11 - - - - - - - l.

'1,."

"

R.

.------'1--,I,,.A

f. f

f


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Use of Complex PlotsFrom a Nyquist plot the damping can be calculated asthe 3 dB points are easily found. However, in practicethe curve will not be a circle and will not pass throughthe zero due to interference of other resonances. but acircle can always be constructed to fit the curve at res-onance. This circle will represent the response from aSingle mode and from this the damping can be calcu-lated.A frequency sweep will give a circle for each reso- ...anance, sometimes making the determination of the res-onance frequencies troublesome. Nyquist plots are 1therefore Ideal for the study of a single resonancewhereas the plots of the complex parts against fre-quency are better suited for. finding the resonance fre- ~ L----=::!!!!;;roor.:-h,.,...::=*... : r , L H ~ . . . . : ; ~ - - - 1 ~quencies. Compared to an amplitude plot, the peaksare narrower and the direction of the peak gives infor-mation of the phase between excitation and response.The curves shown on the figure indicate that the partof the structure on which the measurement Is made, Isvibrating in opposite phases at the two resonance fre-quencies.Modern sine exciter controls have provisions for calcu-lation of the complex functions, presenting these asanalogue signals. When digital analyzers are used thefunctions are calculated from the Information of ampli-tude and phase obtained by measuring the spectra ofexcitation and response.

, . ~ ., U .:a.-:-: . : U(i)_______ O$ M 21


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22

Exc'itation MethodsA vibration exciter Is an excellent means of providing1he force input to t.he structure to be analyzed either byapplying a sine or a broad band signal. In the lattercase the Input as well as the output are measured andanaiyzed using Fast. Fourler Techniques (FFT). The fre-quency response Is calculated from the input spectrum,measured with a force transducer, and the outputspectrum. normally measured with an accelerometer .Instead of using an exciter a broad band excitation canbe produced by an impact hammer integrally mountedwith a force transducer. The impact method is last: theImpulse contains energy at all frequencies and will there -fore excite all modes simultaneously. The set-up time Isminimal and the requirements to the amount of equip-ment are small. However. the signal to noise ratio is poorand for large. fragile structures with a high degree ofdamping it can be impossible to get a sufficiently largeresponse without damaging this test object. The vibra-lion exciter has a high signal to noise ratio. an easycontrol with a choice of excitation waveforms and thepossibility of exciting several points at the same time .Regardless of the eXcitation method the response isstudied as described on the previous pages, and to ob-tain the mode shape either the excitation or the mea-surement of the response should be performed at sever-al pOints on the structure.

....-11 f+""'""--.. ~....~ .,-

:::::- ...

,I,,,,,,

.',,


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Multi-Shaker SystemsUse of more than one exciter can be necessary for thesimple reason of obtaining a larger force or a -distribu-tion of the total force by acting at different points. butmore often multi-shaker syslems are used 10 separatevibration modes.

If a uniform structure Is vibrating in a pure mode allpaints of it will vibrate either in phase or in antlphase.In practice this is only seldom the case. The vibrationis a result of more than one mode, indicated on thecomplex plot by circles not symmetrical to the axis. Byplacing more exciters on the structure their relativeforces can be adjusted to eliminate the vibration due toother modes than that to be studied, indicated by sym-metry of the complex plot.Each mode to be eliminated requires an exciter, but afew exciters will normally be sufficient to produce apractically pure mode. Where only a few exciters areneeded it Is possible to adjust their forces manually toobtain the phase or anti phase response, but for largersystems the setting-up of the exciters as well as the datatreatment is computerized.

1 point~ x c i t a t i o n

4 pointexcitation23


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We hope this booklet has answered a lot of questions to r you andwill continue to serve as a handy reference guide. If you have otherquestions about measurement techniques or instrumentation.please contact one of our local representatives, or write directly to:BrOel & Kj.r2850 N.rumDenmark


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Bruel & KjserDK2850 N.

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