Vibro-acoustic analysis of noise generation from a full scale model

Vibro-acoustic analysis of noise generation from a full scale model ofmodular bridge expansion joint

Jhabindra P. Ghimirea), Yasunao Matsumotob) and Hiroki Yamaguchic)

(Received: 28 February 2008; Revised: 28 August 2008; Accepted: 1 September 2008)

Noises generated from modular bridge expansion joints during vehicle pass-byshave been causing local environmental problems recently. Previous experimentalstudies showed that possible causes of dominant noise components generatedfrom the bottom side of the joint might be different from those from the top side.The objective of this study was to obtain theoretical insights into the mechanismof noise generation from the bottom side of the joint for which a main noisesource might be structural vibration of the joint. Vibro-acoustic analysis wasconducted based on the information from a full-scale model of modularexpansion joint obtained in previous experimental studies. The dynamicbehavior of the joint model was investigated by using the finite element method(FEM) and the sound field inside the cavity located beneath the joint model wasanalyzed by using the boundary element method (BEM). Indirect BEM wasused to calculate the sound pressure inside the cavity with the velocity responseobtained by the FE analysis as a boundary condition. The frequency rangeconsidered in the analysis was 20–400 Hz where dominant frequencycomponents were observed in the noise measured in the cavity beneath the jointin the previous experiment. It was intended to interpret numerical resultsobtained by a model developed with available mechanical properties of the jointcomponents to seek a general understanding of the noise generation mechanismof the modular expansion joint. It was observed that the peaks in the spectrumof noise inside the cavity were due to resonances of structural vibration modes ofthe joint and/or resonances of acoustic modes of the cavity. There was evidencethat showed possible interaction between structural modes of the joint and theacoustic modes of the cavity. © 2008 Institute of Noise Control Engineering.

Primary subject classification: 21.2.2; Secondary subject classification: 75

1 INTRODUCTION

Bridges constructed recently tend to have longer andcontinuous-type spans owing to advanced technologyin bridge construction, such as cable-supported typebridges and base-isolated viaducts. Those bridgesrequire greater movement capability in multi-dimension for bridge expansion joints. Modular bridgeexpansion joint allows greater movements in transla-tion and rotation required by long and continuous span

a) Civil and Environmental Engineering, Saitama University,255 Shimo-Ohkuo, Sakura, Saitama, 338-8570, JAPAN

b) Civil and Environmental Engineering, Saitama University,255 Shimo-Ohkuo, Sakura, Saitama, 338-8570, JAPAN,email: [email protected]

c) Civil and Environmental Engineering, Saitama University,255 Shimo-Ohkuo, Sakura, Saitama, 338-8570, JAPAN,email: [email protected]

442 Noise Control Eng. J. 56 (6), Nov-Dec 2008

bridges. The main components of the joint consists of aset of several parallel steel I-beams (referred to ascenter beams in this paper) aligned perpendicular to thebridge longitudinal axis, which is supported by a set ofseveral parallel steel H-beams (referred to as supportbeams) in parallel with the bridge axis. This structuredivides the total movement required for the joint intosmall movements required to accommodate each gapbetween the center beams. Because of this advantage,the application of the modular expansion joint has beenincreased these days. However, it has been recognizedthat the modular bridge expansion joint causes noise asvehicles pass over it1 and that noise has inducedregional environmental problems recently in Japan andelsewhere2.

Although possible techniques to reduce noise gener-ated from the modular bridge expansion joint havebeen reported, e.g., Fobo3, the mechanism of noisegeneration from the modular bridge expansion joint has

not been understood fully. A series of studies haveinvestigated possible noise generation mechanism ofthe modular expansion joint by conducting noise andvibration measurements with a full-scale joint modelduring car pass-by along with impact testing of thejoint model4,5. Finite element analysis of the jointmodel was also conducted to understand the dynamiccharacteristics of the joint model5. It was concludedfrom these studies that the noise generated from the topside of the joint may be related to resonances of aircolumn within the gap formed by a rubber sealingbetween two adjacent center beams and a car tire. Thenoise generated from the bottom side of the joint maybe attributed to sound radiation from vibrations of thejoint structure, such as the center beams. Thosefindings imply that, in a practical noise controlproblem, sources of joint noise may be dependent onthe location of receiver. For example, in low-riseresidential buildings along viaducts that are quitecommon in congested cities, residents may be affectedmainly by the noise generated from the bottom side ofthe joint.

If the noise generation from the bottom side of thejoint is caused by vibration of the joint structure, under-standing of the dynamic characteristics of the jointstructure can be useful to develop effective measuresfor noise reduction. The dynamic response of themodular expansion joint subjected to traffic loadingwas investigated analytically by Steenbergen6 andexperimentally by Ancich et al.7, although the objectiveof these studies was to investigate the durability of thejoint structure exposed to repeated dynamic loadingsdue to vehicle pass-bys.

In relation to the mechanism of the noise generationfrom the bottom side of modular expansion joint,Ancich and Brown2 measured noise and vibration ofmodular expansion joints installed in bridges anddiscussed the possibility of the interaction betweenstructural vibration modes of the joint and acousticmodes of the cavity located beneath the joint. Theyreported the effectiveness of a Helmholtz absorberinstallation into the cavity beneath the joint in noisereduction, which implies possible contribution ofacoustic modes of the cavity to noise generation.

The objective of this study was to obtain theoreticalinsights into the contribution of the vibro-acousticcharacteristics of a system consisting of the modularexpansion joint and the cavity beneath the joint to thenoise generation from the bottom side of the joint.Numerical vibro-acoustic analysis of the full-scalejoint model used in the previous studies4,5 wasconducted by using finite element method (FEM) /boundary element method (BEM) approach. FEM wasused to calculate the dynamic response of the expan-

Noise Control Eng. J. 56 (6), Nov-Dec 2008

sion joint and indirect BEM was used for acousticanalysis of the cavity beneath the joint. A numericalmodel was developed based on available mechanicalproperties of the joint components. Assumptions weremade for model properties that were not available inliterature and other sources. From the numerical resultsobtained in such a manner, it was intended to obtainunderstanding of the noise generation mechanism thatcan be applied to modular expansion joint in general. Inparticular, possible mechanisms of noise generationfrom the bottom side of the joint were discussed basedon structural vibration modes of the joint and acousticmodes of the cavity.

2 FULL SCALE JOINT MODEL ANDEXPERIMENT

Figure 1 shows the full scale joint model used in theprevious studies4,5. The joint model was set up in thecompound of the Kawaguchi Metal Industries Co., Ltd.in Saitama, Japan. The joint model consisted of threecenter beams that were supported by four supportbeams. Control mechanisms consisting of a steel plank(referred to as control beam) and rubber springsinstalled between the top surface of a control beam andthe bottom flange of a center beam were designed toprevent excessive displacement between the two centerbeams. There were steel frames placed vertically toaccommodate rubber springs between the frame andthe bottom flange of a support beam and a polyamidebearing between the bottom flange of a center beamand the top flange of a support beam. There were polya-mide bearings beneath the ends of the support beamsand rubber springs placed on top of the ends of supportbeams. Additionally, the modular bridge expansionjoint has a drainage capability with the installation of arubber sealing into each gap between two adjacentcenter beams. The joint model was mounted on top ofa test cavity constructed under the ground level torepresent the cavity beneath the joint between adjacentbridge girders in real bridges (Fig. 2). There was an

Fig. 1—Plan and cross section of full-scale testjoint model.

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opening at each end of the cavity. The wall of the cavitywas covered by the Styrofoam that provided soundabsorption within the cavity.

In order to identify the dynamic characteristics ofthe joint, impact testing was carried out in the previousstudy5. The vertical and lateral acceleration of thecenter beams were measured at different locations and,additionally, the sound pressure was measured insidethe cavity beneath the joint at 1.0 m below the topsurface of the center of the joint. Several measurementswere carried out by impacting the center beam from thetop at different locations. The details of the experimen-tal procedure and the results of experimental modalanalysis were presented in Ravshanovich et al.5 A trans-fer function was calculated by using the impact forcemeasured by an impact hammer as input and the accel-eration of the beam or the sound pressure inside thecavity as output.

3 VIBRO-ACOUSTIC ANALYSIS OF FULLSCALE MODEL

3.1 Analysis Procedure

In the vibro-acoustic analysis conducted in thisstudy, firstly, a finite element model of the full-scalejoint model was developed so as to identify the modal

Fig. 2—Cross-sectional views of the cavity be-neath the joint.

Table 1—Cross-section, size and materials for stee

Center beamCross-section (mm) I-shape, 140�80�21�12Young’s Modulus �N/m2� 2.06�1011

Poisson ratio 0.3

Table 2—Spring constants of bearings and springs.

Center beams

Polyamide bearing Rubber spring PolyVertical (N/m) 5.67�108 1.50�106

Lateral (N/m) 2.02�108 5.07�105

Torsion (Nm) 3.94�106 9.76�103

Rotation (Nm) 2.15�105 5.56�102


parameters of the joint. The velocity responses of thejoint to different point loadings were then calculated bymodal superposition to compare the numerical resultswith the experimental results from the impact testing.Finally, the velocity response obtained was used as theboundary condition in the boundary element analysisof acoustic field in the cavity beneath the joint.

3.2 Finite Element Analysis of ExpansionJoint

3.2.1 Model description

Figure 3 shows the FE model of the joint developedin this study. The center beams, the support beams, thecontrol beams and the frames were modeled with shellelements so that the vibration response of the jointcould be transferred directly to the boundary elementmodel as velocity boundary condition. Bearings andrubber springs were simplified and modeled withspring elements as in the FE model developed in theprevious study5. Geometric and material properties of

Spring

Bearing

Frame

Support beam

Center beam

(a) (b)

Fig. 3—FE model of the expansion joint: (a) 3-Dview; (b) Cross-section view.

bers.

Support beam Control beamH-shape, 120�90�20�12 Rectangular, 80�25

2.06�1011 2.06�1011

0.3 0.3

Support beams

Control beams Control springe bearing Rubber spring�108 5.83�106 3.52�105

0 1.97�106 1.19�105

0 3.89�104 2.32�103

0 2.27�103 1.34�102

l mem

.5

amid5.97

different components in the FE joint model are shownin Tables 1 and 2. The size of a typical FE mesh forshell elements in the analysis was 40 mm to representthe cross section of the structural components of thejoint, such as the center beams (Fig. 3). The ANSYS10.0 was used in the analysis described in this section.

3.2.2 Velocity response

Velocity response of the expansion joint was calcu-lated with harmonic point loads of unit magnitude inthe frequency range from 20 to 400 Hz with an inter-val of 1 Hz. The point loads were applied in the lateraland vertical directions simultaneously at the center ofthe top flange of the second center beam, as shown inFig. 4, to represent the loading on the joint during theimpact testing experiment. In Fig. 4, the circle mark atthe center of the third center beam represents one of themeasurement positions during the impact testing, andthe data at this location was used for comparisonbetween numerical and experimental results in thispaper, as an example. Modal-based forced responseanalysis was carried out by using the structural modesidentified as described in the preceding section. All 211structural vibration modes identified from the FEanalysis in the frequency range between 0–800 Hzwere considered in the analysis, since structural modesup to a frequency approximately double the maximumfrequency of interest should be considered in theresponse calculation8. A modal damping ratio of 1%was assumed for all structural modes considered. Thevelocity response was calculated at all nodes of the FEmodel. The LMS Virtual Lab Rev 6A was used in theanalysis described in this section.

3.3 Boundary Element Analysis of AcousticField

The velocity response obtained in the FE analysis asdescribed above was used as a boundary condition in

Point Loads

Z

Y

X

Third centerbeam

Fig. 4—Position and direction of point loads forvelocity response evaluation.


BE analysis of the acoustic field in the cavity beneaththe joint. The BE model of the cavity developed in thisstudy is shown in Fig. 5. The boundary of the cavitywas discretized into quadrilateral and triangularelements. The maximum size of acoustic boundaryelement was set as 100 mm so that the maximumfrequency that could be analyzed was 566 Hz accord-ing to a general recommendation that an accepted meshsize would be less than one-sixth of shortestwavelength of interest. The top boundary of the BEmodel was exactly the same as the FE model of thejoint so that the velocity response of the joint could betransferred directly to the BE model. In this analysis, itwas assumed that vibration response calculated fromthe in vacuo structural modes of the joint calculatedseparately can be used to analyze the acoustic field inthe cavity, i.e., a weak coupling was assumed betweenthe expansion joint and cavity beneath it (the dynamicbehavior of the expansion joint was not influenced bythe fluid in the cavity)9. According to the informationreceived from the manufacturer of the Styrofoam, thesound absorption capacity of the Styrofoam was low inthe frequency below 500 Hz. Therefore, the effect ofthe Styrofoam attached to the walls of the cavitybeneath the joint was not considered in the analysis.The bare walls and floor of the cavity were consideredrigid in the model. This assumption reduced computa-tional cost in the numerical analysis. The sound speedand the density of the air used in the BE analysis were340 m/s and 1.225 kg/m3, respectively.

Modal acoustic transfer vector (MATV) technique inindirect BEM (IBEM) was used to calculate the soundpressure inside the cavity. In this method, acoustictransfer vectors (ATVs), which are the transferfunctions relating the normal velocities at the boundaryto the sound pressure at a measurement point (i.e., afield point), were calculated. Modal parameters and

(a) (b)

1 m

Openings

Joint-cavityboundary

Y

XZ

Measurement point

Fig. 5—Boundary element model of the cavity foracoustic analysis: (a) Full 3-D model; (b)Sectional view showing measurementpoint.

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modal participation factors of structural modes werethen used to calculate the sound pressure at a fieldpoint. The details of ATV and MATV can be found inliterature8,10. The field point used in this analysis was atthe center of the cavity and 1.0 meter below the topsurface of the joint: this point was equivalent to themeasurement location for sound pressure in the impacttesting experiment. The frequency range considered forthe acoustic analysis was 20–400 Hz. The LMS VirtualLab Rev 6A was used for the acoustic analysis.

3.4 Finite Element Modal Analysis of theCavity Beneath the Joint

Finite element analysis of the cavity beneath thejoint shown in Fig. 2 was conducted to identify theacoustic modal parameters of the cavity. The FE modelof the cavity developed is shown in Fig. 6. The acousticspace inside the cavity was modeled by cubical fluidelement of mesh size 130 mm so that acoustic modeshaving natural frequencies up to 435 Hz could becalculated based on the relation between the mesh sizeand the highest frequency as described above. Theopenings on both sides of the cavity were modeled byapplying impedance boundary condition. A character-istic acoustic impedance of 416 kg/m2 s (i.e., theproduct of the sound speed and the air density usedabove) was applied to model these openings11.

4 RESULTS

4.1 Velocity Response of the Joint

Figures 7 and 8 show the mobility frequencyresponse functions calculated for the velocity responseat the center of the third center beam (i.e., the locationshown in Fig. 4) in the lateral and vertical directions,

Openings

Y

XZ

Fig. 6—FE model of the cavity for acoustic modalanalysis.


respectively. The peaks in the velocity responses of thejoint calculated in the numerical analysis were attrib-uted to vibration modes of the joint structure. Forexample, the peaks in the numerical results at 112 Hzand 161 Hz in the lateral response were interpreted asthe excitation of lateral bending modes of the centerbeam at 111.97 Hz and 161.49 Hz, respectively. Thesemodes had one of the anti-nodes at the loading point,i.e., the center of the second center beam. For the verti-cal response, the peaks in the numerical results at160 Hz, 189 Hz, and 241 Hz were due to the excitationof structural modes at 160.35 Hz, 189.35 Hz and241.59 Hz, respectively. These modes had dominantvertical bending of the center beams with one of theanti-nodes at the loading point.

Figures 7 and 8 also show the corresponding experi-mental data5. Two sets of experimental data arepresented to show the repeatability of the measure-ment: the measurement appeared to be highly repeat-able at frequencies below 300 Hz. Although similartrend could be observed in the experimental and

Fig. 7—Velocity response at the measurementpoint in lateral direction. Key:¯¯¯¯,model;——, experiment-1;——,experiment-2.

Fig. 8—Velocity response at the measurementpoint in vertical direction. Key:¯¯¯¯,model;——, experiment-1;——,experiment-2.

numerical results of the velocity responses, there werediscrepancies in the magnitude and the peak frequen-cies of the response. Possible reasons include errors inthe modeling of the expansion joint, for example,errors in the spring constants used for rubber bearingsand springs, and errors in the damping ratio chosen inthe response calculation. Also, the loadings exerted bythe impact hammer might not have been applied to thecenter beam at 45 degrees from the ground surface asin the numerical analysis.

4.2 Sound Pressure Response Inside theCavity

The numerical frequency response function betweenthe sound pressure in the cavity and the input force isshown in Fig. 9. Additionally, the natural frequencies ofthe vibration modes of the joint and the acoustic modesof the cavity are indicated in Fig. 9 for comparison withthe peak frequencies in the frequency responsefunction. The peak frequencies in the noise appeared tocorrespond to the natural frequencies of the vibrationmodes of the joint, the natural frequencies of acousticmodes of the cavity, or both. This comparison isdiscussed in a later part of this paper.

In the figure, the numerical result is compared withthe experimental data measured in the impact testing5.Two sets of experimental data in Fig. 9 show that themeasurement appeared to be repeatable at frequencieshigher than about 120 Hz. Although a similar trendcould be observed in the experimental and numericalresults, there were discrepancies in the magnitude andthe peak frequencies of the frequency responsefunctions for several possible reasons. The discrepan-cies in the peak frequencies of the frequency responsefunction calculated for the sound pressure, compared to

Fig. 9—Sound pressure inside the cavity andnatural frequencies of structural andacoustic modes. Key:¯¯¯¯,model;——, experiment-1;——,experiment-2;�, structural mode;�,acoustic mode.


the corresponding experimental data, may be partly dueto differences in the natural frequencies of the vibrationmodes of the joint between the experimental andnumerical results as discussed in the previous section.Additionally, there might be minor effects of the Styro-foam in the cavity beneath the joint in the experimentaldata, which were neglected in the numerical analysis.Spatial variation of the sound pressure around themeasurement point appeared to be significant at higherfrequencies, according to parametric investigationconducted separately, so that some discrepancies couldbe expected at higher frequencies if the field point forthe numerical calculation of sound pressure was notidentical to the measurement point in the experiment.

5 DISCUSSION

5.1 Sound Generation Mechanism

Sound generation from the interaction of the vibrat-ing structure with the enclosed acoustic cavitydiscussed in previous studies9,12 may be similar tosound generation from the joint model and the cavitybeneath it investigated in this study. According to thoseprevious studies, the peaks in the frequency responsefunction calculated for the sound pressure in the cavity,as observed in Fig. 9, may be attributed to three differ-ent mechanisms: (1) major contribution of structuralmode(s) of the joint with possible minor contributionof acoustic mode(s) of the cavity, (2) significant contri-bution from both structural mode(s) of the joint andacoustic mode(s) of the cavity, and (3) major contribu-tion of acoustic mode(s) of the cavity with possibleminor contribution of structural mode(s).

For example, the peak in the frequency responsefunction for the sound pressure at around 160 Hz inFig. 9 may be attributed to the resonance of the struc-tural mode at 160.35 Hz (vertical bending mode) andthe acoustic modes at 161.10 Hz and 161.71 Hz. Thesestructural and acoustic modes are shown in Fig. 10. Theexcitation of this structural mode was observed in thevelocity response in the vertical direction shown in Fig.8. The acoustic mode at 161.10 Hz shown in Fig. 10had low amplitude at the boundary with the joint so thatthis acoustic mode may have had little interaction withthe structural mode. Although the acoustic mode at161.71 Hz shown in Fig. 10 may have had higher possi-bility of interaction with the structural mode, themagnitude around the measurement point of this acous-tic mode was low. Therefore, the peak in the frequencyresponse function for the sound pressure at around160 Hz may be caused mainly by the excitation of thestructural mode with some minor effects from theacoustic modes. Similar discussion could be made onthe peaks of the frequency response function for the

447

sound pressure at around 112 Hz, 188 Hz, and 230 Hzwhere structural modes may have contributed morethan the acoustic modes.

The sound pressure peak at 268 Hz may be related tothe structural mode of the joint at 267.6 Hz (lateralbending mode) and the acoustic modes at 267.91 Hzand 269.40 Hz. This structural mode and the acousticmodes are shown in Fig. 11. Although the velocityresponse was small at around 266 Hz in Fig. 7 becauseof the small vibration of the third center beam in thestructural mode shown in Fig. 11, this vibration modemay be excited. The acoustic modes at 267.91 Hz and269.40 Hz may be excited by structural vibration of thejoint because of high amplitude at the boundary withthe joint. Therefore, the peak in the frequency response

Fig. 10—Structural and acoustic modes generating160.35 Hz; (b) Acoustic mode at 161.10 H

Fig. 11—Structural and acoustic modes generating267.6 Hz; (b) Acoustic mode at 267.91 H


for the sound pressure at around 268 Hz may have beencaused by the excitation of both the structural andacoustic modes.

For some peaks in the frequency response functionfor the sound pressure, the contribution may be mainlyfrom the resonance of acoustic modes. For example,Fig. 9 shows that there was no structural mode in thefrequency range between 367 Hz and 397 Hz, whilethere were many acoustic modes in this frequencyrange. The sound pressure peak at around 380 Hz couldbe due to the resonance of the acoustic modes at380.38 Hz, 381.86 Hz, and 383.58 Hz, along withmany other acoustic modes around this frequency.Some of the acoustic modes at around 380 Hz areshown in Fig. 12.

nd around 160 Hz: (a) Structural mode atnd (c) Acoustic mode at 161.70 Hz.

nd around 268 Hz: (a) Structural mode atd (c) Acoustic mode at 269.40 Hz.

souz a

souz an

5.2 Reliability of Discussion Based onNumerical Results

There were differences in the frequency responseobserved between the numerical results obtained fromthe model developed in this study and the experimentalresults from the impact testing in the previous study5,as shown in Figs 7–9. The preceding sections showexamples of those differences and discuss possiblecauses. Model updating was not attempted in this studybecause the experimental data available were limitedwhile there were several sets of model properties thatcan be optimized. Although this was the limitation ofthis study, it was assumed that reasonable theoreticalinsights into the noise generation mechanism could beobtained from the model based on the reliable numeri-cal technique with available mechanical properties andassumptions for model properties. The properties ofstructural vibration modes obtained from the numericalmodel were compared with the modal parametersidentified in the impact testing5, although the detailsare not presented in this paper. There was a reasonableagreement between the numerical and experimentalmodal properties in vibration modes dominated byvertical bending of the beams, such as the mode shownin Fig. 10. This may partially support the reliability ofthe discussion based on the numerical results obtainedin this study. However, there were some discrepanciesin vibration modes dominated by lateral motions of thejoint, including rigid body mode and lateral bending. Asimilar conclusion was reported in the previous study5

that compared modal properties identified in theexperimental modal analysis with those in the analyti-cal modal analysis with a 3-D frame model.

Fig. 12—Acoustic modes generating sound aroundmode at 381.86 Hz and (c) Acoustic mode


Figure 13 shows the vertical velocity responses ofthe joint measured at the location shown in Fig. 4during pass-bys of two types of vehicle (i.e., anordinary car and a wagon) at two different speeds (i.e.,40 and 50 km/h)4,5. The right wheels of those vehiclespassed over the measurement and loading point shownin Fig. 4. Dominant frequency components in the verti-cal velocity responses were observed at frequenciesbelow 220 Hz for all the experimental conditions,although there were variations caused by differentconditions, as expected. Comparison of Fig. 13 withFig. 8 shows similar characteristics in the resultsbetween the vehicle pass-by experiment and the impacttesting, such as peaks at about 155 and 185 Hz anddecreases at higher frequencies, although direct

Hz: (a) Acoustic mode at 380.38 Hz; (b) Acoustic83.58 Hz.

Fig. 13—Velocity responses in vertical directionat the measurement point during vehiclepass-bys over control beams. Key:——,ordinary car at 40 km/h;——, ordinarycar at 50 km/h;¯¯¯¯, wagon at40 km/h;-·-··, wagon at 50 km/h.

380at 3

449

comparison cannot be made because Fig. 13 includesthe effect of loading spectra while Fig. 8 shows thefrequency responses. Those similarities observed inFigs 8 and 13 imply that the theoretical insights into thedynamic characteristics of the joint and their interac-tion with the acoustic characteristics of the cavityobtained from impact testing data could be useful innoise control in real situation.

6 CONCLUSIONS

Vibro-acoustic analysis of the full-scale model ofthe modular bridge expansion joint was carried out soas to obtain theoretical insights into the mechanism ofnoise generation from the bottom side of the joint. Inthe numerical analysis, sound field beneath the jointwas investigated by FEM-BEM approach in thefrequency range 20–400 Hz. Modal analysis was alsoconducted so as to understand the dynamic character-istics of the joint structure and the acoustic propertiesof the cavity beneath the joint. It was observed thatdominant frequency components in the sound pressuregenerated inside the cavity was due to vibration modesof the joint structure and/or acoustic modes of thecavity. Some dominant frequency components in thesound pressure inside the cavity beneath the joint maybe caused mainly by the vibration modes of the jointstructure and others may be caused by the excitation ofacoustic modes by the vibration modes of the structure.At higher frequencies where the modal density of theacoustic modes was high, there were dominantfrequency components in the sound pressure that maybe caused mainly by the excitation of acoustic modesof the cavity with minor contribution from vibration
modes of the joint structure.

7 ACKNOWLEDGMENTThe support from the personnel of the Kawaguchi

Metal Industries Co., Ltd. is gratefully acknowledged.

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