Application Note

A Hand-held Exciter for Field Mobility Measurements– an alternative to the impact hammer method

by Svend Gade and Henrik Herlufsen, Brüel & Kjær

AbstractThis Application Note introduces anew excitation technique for excitingmechanical structures, in order tomake mobility measurements. A smallhand-held exciter or shaker has beendeveloped for field measurementsyielding the same advantages as thoseobtained using an impact hammer aswell as those obtained using a shakerfor the frequency response functionmeasurements.

The main advantages are: easy touse in the field, no elaborate fixturing,and best linear approximation of sys-tem under test as well as no leakage,assuming an appropriate excitationsignal has been selected. The only dis-advantage is that some degree of free-dom (DOF) jitter may be introducedusing this method, and the use of thehand-held exciter is only applicable forrelatively small structures. A completereview of advantages/disadvantages ofvarious excitation techniques is includ-ed in this Application Note in order toput the method into the right perspec-tive. 940987/1e

4-channel AnalysisSystem 3557

Responsesignals

Accelerometers

Hand-heldExciter5961

Force Transducer8203

Excitationsignal

GeneratorSignal

Fig.1 Complete measurement set-up using the 4-channel Analysis System Type 3557including a generator, Hand-held Exciter Type 5961 including miniature Force Trans-ducer Type 8203, and up to three accelerometers for measuring response signals

Introduction

In most applications of system anal-ysis or testing, where input-outputrelationships have to be measured, itis necessary to excite the system witha well controlled and measurable in-put. A number of different types ofexcitation signal are available for theanalysis, each having its own advan-tages and disadvantages. For struc-tural testing, for instance, it ispossible to use either an impact ham-mer or a shaker.

If a shaker is selected, there are anumber of generator signals whichcan be used. These are basically di-vided into three types, i.e., random,

Brüel & Kjær B K

deterministic, or transient (impulse/impact) signals. The choice of the sig-nal depends, among other things,upon the test application, non-linearbehaviour of the system and timeavailable for the analysis. If a ham-mer is selected, in fact we only haveone choice, namely transient (impact)excitation, although random impactis sometimes used for zoom or lowfrequency measurements. The practi-cal difference between the use of ashaker or a hammer in the field isthat a shaker is normally in a fixedposition and needs elaborate fixtur-ing; while a hammer is easy to move

from measurement position to meas-urement position. Therefore a hand-held exciter (shaker) will bridge thegap between the two techniques.Such an exciter is easy to move frompoint to point and allows the use ofexcitation signals which are random,deterministic or transient of nature,when a versatile generator is availa-ble. Before we look at the advantagesand disadvantages of the hand-heldexciter we need to review the tradi-tional techniques. In the following itis assumed that DFT/FFT analysishas been used in order to obtain fre-quency response estimates.

Fig. 2 Random signal

Fig. 3 Filtering of the random excitation signal giving better dynamic range in the analysis

Fig. 4 Leakage indicated by a coherence lower than one at the resonance, caused by theHanning weighting when using random excitation

Fig. 5 Both excitation and response signals are shorter than the record length using burstrandom excitation

Random Excitation

A random signal such as that shownin Fig. 2 is a continuous type of signalwhich never repeats itself and whoseamplitude can only be predicted interms of statistical parameters.

The main characteristic of the ran-dom excitation signal is that the spec-tral estimates for each recorded datablock will have random amplitudeand random phase. Thus, at each fre-quency the system can be consideredas being excited by different ampli-tude and phase in each data blockanalysis. Considering the effects ofnon-linearities as noise at the output,the frequency response estimatorH1(f) [Ref.1] will give the best linearfit to the system or the optimum fre-quency response function minimizingthe effects of the non-linearity (alsocalled the least squares estimate).This is a very important advantageof random excitation. Another advan-tage of using random excitation isthat it can be fairly easily shaped tofit the frequency range of interest byfiltering and modulating the originalbroad band signal. Thus the systemis not excited by frequencies outsidethe analysis bandwidth, giving a bet-ter dynamic range in the analysis.Fig. 3 gives an illustration of a base-band and a zoom measurement.

The continuous random signal doesnot fit the block length in the analy-sis. A smooth weighting function(such as the Hanning weighting)therefore has to be applied, whichcauses leakage in the spectral esti-mates [Ref.2]. This is exemplified inFig. 4 and is one of the disadvantagesof random excitation.

As a summary, the main advantageis best linear approximation of thesystem under test, and the main dis-advantage is leakage.

Burst Random Excitation

We can avoid the disadvantage of therandom excitation by using burstrandom excitation i.e. gating the ran-dom signal. If both the excitation andresponse signals are shorter than therecord length (see Fig. 5), we can ap-ply rectangular weighting and themeasurement will be leakage free(see Fig. 6).

For very lightly damped structures,special weighting functions may haveto be applied [Ref.3].

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Fig. 6 Frequency response function estimation is leakage free using burst random exci-tation

Fig. 7 Example of a pseudo-random signal

Fig. 8 Spectrum of a pseudo-random signal

Fig. 9 Leakage free measurement using pseudo-random excitation

Deterministic/Pseudo-random Excitation

The pseudo-random signal is special-ly designed for DFT analysis whichworks on blocks of data. It is madeup of a segment of a random signalof length T which is repeated afterevery period of time T, see Fig. 7. Itis periodic and therefore has energyonly at discrete frequencies f = k/T,where T, is the period length and kis an integer. The period length T ismatched to the record length of theanalyzer, so the frequency compo-nents of the pseudo-random signalscoincide with the computed frequencylines in the analyzer. One recordlength of the pseudo-random signaltherefore contains all the informationin the signal. Rectangular weightingshould be used and there will be noleakage in the spectral estimates.This is probably the main advantageof using pseudo-random excitation.

The signal is designed in such away that each frequency componenthas the same amplitude in the fre-quency range of interest. The phaseangle between the different compo-nents, however, can be a random aswell as a continuous curve. The pseu-do-random signal can therefore alsobe considered as a number of sinewaves, having the same amplitudeand phase from measurement tomeasurement in the analysis fre-quency range, and where the timerecord in the analyzer contains aninteger number of periods for eachsine wave.

The spectrum of the pseudo-ran-dom (deterministic) signal is shownin Fig. 8. As the signals involved aredeterministic and periodic only a fewaverages are needed in the analysis,assuming that there is no extraneousnoise at the input or output. This canbe an advantage especially for lowfrequency work and zoom analysis,compared to random noise excitationwhere some averaging is alwaysneeded in practice. The main advan-tages in using pseudo-random excita-tion are: no leakage in the analysis,the spectrum can be shaped to exciteonly frequencies in the range of in-terest and only a few averages areneeded. The main disadvantage isthat there is no linear approximationof the system under test. A measure-ment example is shown in Fig. 9,which shows the same level at reso-nance as for the burst random exci-tation.

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Fig. 10 Periodic random excitation signal

Fig. 11 Impact hammer and a typical input force pulse

A special type of pseudo-randomsignal, where the crest factor hasbeen minimized is the so-called mul-tisine, where a fast sine sweep is re-peated every time record, T.

Periodic Random Excitation

We can avoid the disadvantage ofpseudo-random excitation by chang-ing the pseudo-random signal se-quence with time. Such a signal iscalled periodic random and consistsof a pseudo-random sequence (A) oflength T which is repeated severaltimes followed by another sequence(B) of length T, which is independentof A, repeated the same number oftimes. A third sequence (C) independ-ent of the previous ones is now re-peated and so on. As indicated inFig. 10, the first couple of periods ofeach sequence are used for the tran-sient response of the system after thechange of sequence i.e. change ofphase and amplitude between all thesine wave components. The last se-quence is then used for the analysiswhere the system is in a quasi-sta-tionary condition. Rectangularweighting should be used and therewill be no leakage. In addition, it willgive the best linear approximation ofthe system, as the different pseudo-random sequences are independent ofeach other (changed randomly inphase and amplitude), and each dif-ferent block of signal may have dif-ferent crest factor.

Transient/Impact Excitation

A very popular and convenient exci-tation technique for mechanicalstructures is impact excitation usingan impact hammer.

Fig. 11 shows an impact hammer,with a force transducer on which animpact tip is mounted. When thestructure is excited by the hammer,energy is transferred to the structurein a very short period of time, givinga typical input force signal as shownin Fig. 11. The shape of this force sig-nal depends upon the type of hammertip, the mass of the hammer and thedynamic characteristics of the struc-ture under investigation. As the fre-quency bandwidth of the forcespectrum is determined by the lengthof the signal, these characteristics

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will determine the upper cut-off fre-quency of the excitation signal. Thestiffer the hammer tip and the struc-ture are, the shorter the signal willbe, and the wider the frequency span.Extra mass on the hammer, shown asdotted lines in Fig. 11, will widen theforce signal and therefore lower thecut-off frequency as well as increasethe excitation force level. The advan-tages of using impact testing are: itis very fast, only a few averages areneeded, no elaborate fixturing as forshaker excitation is required, and itis easy to use in the field. However,the force signal has a high crest fac-tor which can make this techniqueunsuitable for non-linear systems.The limited control of excitationbandwidth is also a disadvantage.The frequency range is always fromDC to some upper frequency limit.Special weighting functions are oftenrequired giving some amount of leak-age, which on the other hand can becompensated for [Refs. 2, 3].

Hand-Held Exciter

As a consequence of all the compro-mises using the different excitationtechniques, a small hand-held exciter(Fig. 12) has been developed, yieldingthe same advantages as using impacttesting: no elaborate fixturing, easyto use in the field, and avoiding themain disadvantage of impact testing,the high crest factor. It features thesame advantages as for normal shak-er excitation that a variety of excita-tion signals are available so that themeasurement can be made: leakagefree, and the best linear approxima-tion of the system under test can beobtained, but avoiding the main dis-advantage of shaker testing, elabo-rate fixturing.

It should be noted that the smallhand-held exciter is an alternative tothe impact hammer and of course isonly applicable to small structures.

Fig. 12 Hand-held Exciter Type 5961 and miniature Force Transducer Type 8203

Fig. 13 Measurement set-up and input force spectrum for random excitation

Fig. 14 Frequency response function and coherence function using random excitation

Design and Specifications of the Hand-held Exciter

The Hand-held Exciter consists of anelectromagnetic exciter driven by abuilt-in battery-operated power am-plifier. The excitation signal is fedinto the exciter via the BNC-connec-tor at the bottom. A spiralled cablewith a length of 1.1 to 4 meters issupplied. The frequency range is typ-ically up to 3.2 kHz with a force rat-ing of 0.5 N (RMS) or approximately5 N peak. The tip is made of steel,although plastic and rubber tips canbe used. The physical dimensions area diameter of 4.5 cm and a height of13 cm, and the weight is about 400grams, without cables and forcetransducer/tip. Brüel & Kjær ForceTransducer Types 8200 and 8203 canbe used, although 8203 is recom-mended.

Measurements

Some mobility measurements havebeen carried out on a small lightlydamped aluminium plate with the di-mensions of 250·300·25 mm. Allmeasurements have been carried outusing Brüel & Kjær MultichannelAnalysis System Type 3550 in a dual-channel configuration although amultichannel configuration as shownin Fig. 1 may be used. This systemincludes a very versatile generator,which can be synchronized with, aswell as operate independent of, theFFT/DFT signal processing. A widerange of signals are available fromthe built-in generator in the AnalysisSystem, such as random, burst ran-dom, pseudo-random, periodic ran-dom, multisine, etc. Force TransducerType 8203 was used.

Random Excitation

Measurement set-up and excitationspectrum are shown in Fig. 13, whilefrequency response and coherencefunctions are shown in Fig. 14.

Note that the excitation spectrumshows a level increase at frequenciesslightly lower than the resonance fre-quency of the structure. That is thecombined resonance of the structureand exciter transducer/tip. At the res-onance we see that the excitationspectrum has a drop due to the im-

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Fig. 15 Measurement set-up and input force spectrum for random excitation in zoom mode

Fig. 16 Frequency response function and coherence function using random excitation inzoom mode

Fig. 17 Measurement set-up and input force for burst random excitation

pedance mismatch between the struc-ture and the shaker. Due to the highmobility at resonance, it is very dif-ficult to feed a force into the struc-ture. In this case one will probablyprefer to use the H2 frequency re-sponse estimator [Ref.1]. The coher-ence shows the traditional low valueat resonance, which is mainly due tothe leakage (and to a certain extentthe above-mentioned signal-to-noiseproblems at input). Also in the leak-age case one will prefer to use H2.One advantage compared to impactexcitation is that we can band limitthe excitation spectrum (zoom). Thisis done around the fifth resonance asshown in Figs. 15 and 16. This is afeature an impact hammer does nothave. Comparison between Figs. 14and 16 indicates that the H2 estima-tor was reasonably close to the cor-rect result in baseband mode, wherethe H1 estimator had a value thatdiffered from H2 by 20 log |H1/H2|= 20 log γ 2 = 20 log (0.418) = -7.5 dB.

Burst Random Excitation

A short burst with a duration of10 ms has been used (Fig. 17). It isclear that the overall RMS level ofexcitation drops by approximately20 dB.

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Fig. 18 shows that the leakage phe-nomena is, if not eliminated, then atleast heavily reduced at the reso-nances. Coherence is still so muchlower than unity at resonances thatwe prefer to use the H2 estimator.Using burst random, our signal-to-noise ratio is no longer optimum,which is clearly revealed at anti-res-onances, where the H2 estimatoreven shows some artificial resonancepeaks. In these regions H1 is superiorto H2. In this case rectangularweighting was used since both exci-tation and response signal had a du-ration of the same order of magnitudeas the record length.

Pseudo-random excitation

Pseudo-random excitation has beenused for the measurements shown inFigs. 19 and 20. Leakage is eliminat-ed at resonances and any drop in thecoherence at these frequencies is dueto the drop in the excitation force. Inour case the pseudo-random excita-tion was the best choice, since we alsoobtained an excellent signal-to-noiseratio in the measurement.

High Mobility Structure

A structure with an extremely highmobility (light damping) has beenused for better visualization of thedifferencies of the various excitationsignals.

In more practical situations we willencounter structures exhibiting moredamping, making the measurementseasier to perform yielding results notshowing these extreme drops in thecoherence functions and excitationspectra as seen through Figs. 13 to21.

Fig. 18 Frequency response function and coherence using burst random excitation

Fig. 19 Measurement set-up and input force for pseudo-random excitation

Fig. 20 Frequency response function and coherence using pseudo-random excitation

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Volcano effect

Another effect which is due to thehigh mobility at resonances is thevolcano effect where H1 might evenshow a drop at the resonances, whileH2 eliminates this problem (Fig. 21).Furthermore it seems that one curefor this problem is to apply somebeeswax or silicone grease at the ex-citation point. This will prevent thetip from slipping on the surface. Thisalso reduces the risk of excitation ofdegree of freedom jitter.

Choice of Tips

Since the generator only outputs en-ergy in the analysis range, there isbasically no need for a choice betweendifferent tips. A tip which is stiff

(steel) and which has a small contactsurface is preferable, and if the sur-face allows, you might even use astud like the one shown in Fig. 22.

Conclusion

The Hand-held Exciter Type 5961combines the advantages of an im-pact hammer test and a shaker test.It gives the versatility of the shakertest for optimizing the crest factorand frequency range. This is impor-tant in cases where non-linearities ina structure could be invoked due tothe high crest factor of impact exci-tation. The frequency range of the ex-citation is also optimal, as it can beset to be the same as the frequencyrange of analysis (including zoom).For lightly damped structures, thereis a tendency that the H2 estimator

is the best choice. The main use isfor modal tests on small (and medi-um) size structures.

References

[1] Herlufsen, H.: Dual-channel FFTAnalysis (Part I & II) B&K Tech-nical Reviews, Nos. 1 and 2, 1984

[2] Gade, S. and Herlufsen, H.: Useof Weighting Functions in DFT/FFT Analysis Brüel & Kjær Tech-nical Reviews Nos. 3 and 4, 1987

[3] Gade, S. and Herlufsen, H.: Dig-ital Filter Techniques vs FFTTechniques for Damping Meas-urements Proceedings of 8th In-ternational Modal AnalysisConference, Orlando, Fl, pp1056–064, 1990, also printed inSound and Vibration, pp 24-32,March 1990.

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Fig. 21 Volcano effect Fig. 22 A probe used as a tip for the hand-held exciter