train-inducedfluctuatingpressureandresultantdynamic...

Research ArticleTrain-Induced Fluctuating Pressure and Resultant DynamicResponse of Semienclosed Sound Barriers

Jing Zheng12 Qingliang Li3 Xiaozhen Li 12 and Yunke Luo12

1School of Civil Engineering Southwest Jiaotong University Chengdu 610031 China2MOE Key Laboratory of High-Speed Railway Engineering Southwest Jiaotong University Chengdu 610031 China3China Railway Eryuan Engineering Group Co Ltd Chongqing 400023 China

Correspondence should be addressed to Xiaozhen Li xzhliswjtueducn

Received 4 July 2019 Revised 30 July 2020 Accepted 7 September 2020 Published 22 September 2020

Academic Editor Nuno M Maia

Copyright copy 2020 Jing Zheng et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

is paper reports on train-induced fluctuating pressure and consequent dynamic response of semienclosed sound barriers(SESBs) a novel type of sound barriers A computational fluid dynamic (CFD) model and a finite element (FE) model wereestablished e in situ vibration measurement of the SESB was introduced for the first time Pressure-induced vibrations wereextracted from the measured results e analyzing process of the pressure-induced vibration below 20Hz is verified Influencingfactors of the pressure and vibrations including train running on the near- or far-line and the length effect of total top plates werefinally discussed with the dimensionless method Results show that the distribution of pressure is significantly different but thevibration laws are similar whether the train is running on the near- or far-line e longer is the total length of the top plates thelarger are the pressure and vibration on the inner surface

1 Introduction

Troubles of environmental noise and vibration triggered byrail transit have attracted a significant amount of researchinterests recently [1ndash5] e wheel-rail noise is predominantin overall noise with the train running at a speed lower than300 kmh [6] Sound barriers which have been widely in-stalled along trackside location all over the world are ef-fective in the noise reduction of rail transit by blocking directsound propagation [7] In China some new-style soundbarriers such as fully enclosed or semienclosed soundbarriers (SESBs) have been applied in trackside engineeringto attenuate noise in some demanding regions [8] Manyresearch studies and exploration have been done on theacoustical performance of conventional and novel soundbarriers in the available literature [9ndash12] however thestudies on vibration characteristics of sound barriers es-pecially novel ones were limited e violent vibrations ofsound barriers with the train speeding up which may bringabout the linked bolts falling off structural fatigue damageand displacement of insulation plates may affect the safe

operation of the train result in structural noise radiationand even reduce the noise reduction effect of sound barriersAccordingly correctly evaluating the vibration response ofsound barrier structures is relevant for these technical issues

If the natural wind impact is not considered the vi-bration of sound barriers on high-speed railway bridgesarises from wheel-rail interaction as well as aerodynamicaction related to the pressure fluctuation generated by thetransiting train [13] e analysis methods to predict thewheel-rail interaction are often based on the vehicle-trackdynamic coupling vibration taking track roughness as thesource of the dynamic force considering the vehicle as amultibody system composed of carriage body bogie pri-mary suspension secondary suspension and wheels solvingthe dynamic equations of vehicles rails and bridges throughthe finite element model and dynamic theory Li et al solvedthe vibration response of track bridges in time domain byestablishing the dynamic equations of vehicles tracks andbridges with the Newmark-β method [14] Wu andompson [15] solved the vibration response of box-girderbridges in frequency domain by the dynamic compliance

HindawiShock and VibrationVolume 2020 Article ID 6901564 16 pageshttpsdoiorg10115520206901564

method For recommending the most suitable model infurther prediction Li et al [16] compared the computationcost and accuracy of results obtained from the mode su-perposition method in the time domain and power flowmodels for the vehicle-rail-bridge coupled system areestablished in the frequency domain Zhang and Xia [17]conducted dynamic analysis of the coupled vehicle-bridgesystem based on the intersystem iteration method esemethods all above are often applied in the vibration andvibroacoustic analysis of the coupled system When soundbarriers installed on bridges these methods are still appli-cable Li and Liang [18] investigated the influence of dif-ferent track structures on the vibration and structure-bornenoise of elevated concrete box girders with the frequency-domain theoretical model of the vehicle-track coupledsystem Song and Li [19] compared the effects of three noisemitigation measures on noise control installation of a noisebarrier use of a rail pad with a lower stiffness and adoptingof a floating ladder track With the train speeding upaerodynamic action and its resultant vibration of soundbarrier cannot be ignored Many related research studiesincluding basic studies aiming at the qualitative descriptionof the pressure fluctuation frequency-domain distributionof fluctuating wind and pressure-induced vibration re-sponse have been carried out e general rules of fluctu-ating wind pressure versus time and its related factors wereexplored through scale measurements in situ tests andnumerical simulations [20ndash23] Consistent conclusionsyielded from these studies are that the pressure time historycurve includes the head pulse with a positive peak followedby a asymmetric negative peak appearing at the headstockpassage the small amplitude pressure fluctuation caused bythe intercarriage gaps and the tail pulse with a negative and apositive amplitude as a sequence of the tailstock passageepeak pressure is related to train speed vehicle type anddistance from sound barrier to the train Yang et al [24]decomposed the fluctuating pressure signal collected in afield test targeting at a sound barrier in different frequencybands and figured out that the surface pressure componentin frequency band (0ndash25Hz) is large while that in higherfrequency band (5ndash10Hz) is relatively small Lu et al [25]figured out that the frequency component of the aerody-namic load is less than 10Hz Carassale and Marre Bru-nenghi [26] carried out an open-air experiment to separatethe dynamic response of the aerodynamic forces on atrackside steel frame from the effect of the seismic actioncaused by the train transit According to Carassale the headpulse and the tail pulse on the frequency map have a peakfrequency of about 58Hz Luo and Zhang and Xia [27 28]derived the calculation formulas for change of wind loadacting on the car-body for a l0-span simply supportedU-shaped girder bridge with 100m long double-side 35mbarrier and analyzed the influence of sudden change of windload on the running safety of the train when a train movesinto or out of the wind barrier structure

Most of mentioned studies are aimed at some othertrackside structures or sound barriers with simple structuressuch as vertical sound barriers or simple barriers with lowheight whereas for semienclosed sound barriers (SESBs)

with complicated structure the train-induced fluctuatingpressure and its resultant dynamic response have not beenwell studied

is paper aims to bridge this gap by describing theprocedures of a battery of experimental and numerical in-vestigations carried out on a SESB arranged on a high-speedrailway bridge Firstly train-induced fluctuating pressureand its consequent vibration were simulated numericallyand then the vibration test of SESB is introduced esimulated results were compared with the processed mea-sured results for model validation e verified models werefinally applied to carry out parameter studies to investigateand discuss the influences of operating lines and total lengthof top unit plates on the aerodynamic pressure and dynamicresponse of the barrier e results are of major importanceand subsequently be used (1) to extract the pressure-inducedvibration from original vibration signals according to thefrequency component of fluctuating pressure (2) to obtainthe distribution law of fluctuating pressure at different lo-cations of the SESB under different factors and (3) to derivea fundamental understanding of the vibration responseinduced by fluctuating pressure of high-speed passing trains

e composition of the SESB the CFD model for train-induced fluctuating pressure and the FEmodel for pressure-induced vibration were built respectively in Section 2 esetup of vibration test and main experimental results wereset out in Section 3 en in Section 4 the CFD and FEnumerical models were verified Parameter studies werefinally carried out in Section 5 to discuss the characteristicsof fluctuating pressure and resultant dynamic response ofthe SESB

2 Calculating Models

21-e Semienclosed SoundBarrier e target SESB is fixedon the flanges of the 326m long dual-track simply sup-ported box-girder viaduct of the Hang Zhou-Changshapassenger dedicated line China e cross section of thebarrier and the bridge girder below it are illustrated inFigure 1 e SESB is 815m in height 117m in width and15 km in length and its main structures with 2m intervalswere steel frames composed of bilateral erect steel studs andtop crossbeams To improve the stability of the steel frameslongitudinal bracings are arranged at different heights alongthe longitudinal direction e main noise reduction com-ponents of the SESB are the metal sound insulation platesand transparent PC plates installed on the barrier e steelstuds and crossbeams are H-shaped steel with a dimensionof 300mmtimes 300mmtimes 10mmtimes 15mm Metal plates on theclosed side of the SESB as shown in Figure 2 are 0140mthick and 045m or 05m wide and the PC ones are 002mthick and 11m wide on the side and 104m wide on the topA total of 14 plates are inserted between the flange of H-typeerect steel studs and stuffed rubber into interstices betweenthe plates and the flange of H-type studs On the top cornerof SESB a curved PC plate with 099m radius was installedere are 6 PC plates arranged between every two adjacentcrossbeams For further discussion the track near theenclosed side of barrier is defined as the near-line and on the

2 Shock and Vibration

contrary the other one is defined as the far-line Each twoadjacent steel columns are regarded as a span of the barrier

22 CFD Model

221 Calculation Method When a high-speed train entersthe SESB wind fluctuating pressure will be generated estandard k sim ε two-equation turbulent model and the three-dimensional unsteady uncompressible RANS equation aresolved by FLUENT software to simulate the train windfluctuation on the inner surface of the SESB In the process ofestablishing the CFD model the grid model of the vehicleand SESB is firstly established (described in detail in Section222) and then the size of the calculation domain is de-termined in which the dynamic subdomain and the staticregions are divided the boundary conditions are defined

222 Models of Train and SESB e train model used inthis paper is China Railways High-Speed 380B (CRH380B)e headstock and tailstock are 257m long and everymidcarriage is 25m longe height and width of CRH380Bare 389m and 326m respectively e fluctuating pressurewave mainly consists of head pulse and tail pulse induced bythe passing headstock and tailstock of the train ereforethe aerodynamic behavior of three car models a lead car amiddle car and a tail car are very similar with that of eightcarriage models or sixteen carriage models To furthersimplify the computational model the train model isproperly simplified neglecting bogies doors of the train andtop pantograph and in addition smoothing outer surface ofthe train as shown in Figure 3(a)

A CFD model of the SESB was built by establishing theplates with a whole shell which is smoothed Furthermore

Open

Side

Box girder

Simply supported box girder

Closed

Side Longitudinal bracings

Crossbeams

Eract steel studs

Metal plates

PC plates

Figure 1 Target semienclosed noise barrier

Near line Far line

11700

990 3480 104010401040 1040 10401040 990

8150

(a)

2000 2000 2000 2000

(b)

2000 2000 2000 2000

1170

090

010

4010

4010

4010

4010

4010

4034

8099

0

(c)

Figure 2 Dimensions of target semienclosed noise barrier (a) cross section (b) elevations (c) top view (unit mm)

Shock and Vibration 3

the components such as the track track slab ballast andlower parts of the box girder were neglected in the CFDmodel e simplified model of SESB is exhibited inFigure 3(b)

223 Boundary Conditions For this model the size ofcomputational domain is 3675m times 1681 m times 877m asshown in Figure 4 In computational domain as shown inFigure 5 the vehicle is set to be the dynamic subdomainthe sound barrier is specified to be the static regions andthe contact face is defined as an interface between the twoareas e boundary conditions of the end surfaces whereair flows in and out of the computational domain arespecified to be the pressure far field For the computa-tional accuracy and efficiency the layering mesh methodis applied in the following study In this grid updatingmethod the computational domain will be divided intosmaller subdomains in which grid reconstruction is easierbecause of fewer grids and the static girds at the end of themoving region will be destroyed and created to establishthe expected motion of high-speed trains When thedynamic subdomain moves forward its front part com-presses grids and the rear part stretches the grids e gridheight 05 in dynamic subdomain decides the time ofgrids creating and destroying and the grid destroyingcoefficient is 02 and the grid splitting coefficient is 04e computational domain is generated totally bystructured hexahedron grid A finer grid is used in the areanear the surface of the carriage and the SESB e RANSmethod of wall function is used to simulate the boundary

layer region e thickness of finest grid on the boundarylayer is 00012m e dimensionless y + for the first nodefrom the walls is 100 and the grid growth factor ofboundary layer is 11 Except for the cavity of junction andendpoint quality of the majority exceeds 05 e wholemodel is summed up to 462 million nodes and 440million cells Grid independence test result shows that theaverage pressure on the monitoring surface obtained byfurther densifying the grid has little change and thecurrent model is accurate enough to ensure the validity ofthe calculated results

761m

247m257m

(a)

Bridge deck

815

m

117m

389

m

025

m

326m

624m

Noise insulation plates

(b)

Figure 3 CFD Model of SESB (a) simplified high-speed train model (b) dimensions and cross section of train and noise barrier

1681m

3675m87

7m

Y

X Z

Figure 4 Model of high-speed train


e initial location of high-speed train is 50m away fromthe measured section of the barrier e time step is 0005 sand 600 steps in total are calculated During the progress thespeed of train is set to be 330 kmh on the near-line for thevalidation of the simulated model and 350 kmh on the near-and far-line for parameter analysis e fluctuating pressureon the inner surface of the SESB is explored by the CFDmodel and the layout of monitoring faces on the SESB isshown in Figure 6 to capture their average pressure at eachtime step

23 FEModel forVibrationAnalysis e ABAQUS softwarewas adopted to establish the FE models of vibration re-sponses analysis of SESB under fluctuating pressures As thefluctuating pressure was loaded on the inner surface andbox-girder bridge was not subjected to this load concretebases under the steel studs instead of the box-girder bridgewere established as the foundation of SESB and weremodelled with eight-node 3D brick elements (C3D8R) eroots of steel studs were fixed on the concrete bases Steelstuds were modelled with four-node shell elements (S4R) aswell as the crossbeams and the plates As the fluctuatingpressure-induced vibration is mainly consisted of low-fre-quency one the rubbers stuffed between every two adjacentplates and in the interspaces from plates to steel studs can beomitted because the rubber damping pads can hardly dampvibration of low frequency e total FE model is shown inFigure 7(a) and its size is consistent with design drawings ofSESB e calculated pressure is expanded from the CFDsimulated results of themiddle carriage to the pressure of themiddle six carriages they are combined with the head andtail pulse to form the pressure of the eight marshalled trainand they are applied to all the plates in a span on the SESBaccording to Figure 6 Fluctuating pressure is also applied tothe plates on adjacent spans considering the time interval oftrains passing through different spans of the SESB einstantaneous vibration responses such as the dynamicdisplacement of SESB under pressure can be solved InSection 4 the calculated results will be compared with themeasured ones to verify the applicability of the CFD modeland FE model

Table 1 tabulates all the material properties of this modelFigures 7(b) and 7(c) present the typical modal vibrationshape of SESB and the first 10 modes of natural frequenciesare listed in Table 2 e first mode showing transversedeformation of the SESB is at 4Hz and the vertical bendingmode is above 545Hz Whether pressure-induced reso-nance occurs will be analyzed in Section 32

3 Schemed Field Test

31 Testing Instrumentation A field test was conducted toobtain the vibration response of the target SESB During thetest three variables were continuously recorded the trainspeeds the location of the moving train vibration accel-eration orthogonal to the test surface by means of a velo-cimeter 5 accelerometers and a dynamic data acquisitioninstrument Additional information is given below on thelocation and installation of the monitoring systems

311 Accelerometers e CA-YD-181 piezoelectric typeaccelerometers were used to collect the vibration signals Atotal of about 5 accelerometers were monitored on thebarrier at the midspan of the bridge Accelerometers wereinstalled through a moving crane as shown in Figures 8(a)and 8(b) which display the distribution and specific loca-tions of accelerometers V1 and V2 were arranged on thesteel stud of the closed side of the SESB at 73m and 15mhigh from the root respectively which were the same heightwith the top of No13 plate and No 3 plate respectively V3V4 and V5 were measuring points on the open side whichwere located at 73m 58m and 445m high from the root ofnoise barrier respectively the same height with the top ofNo 13 No 10 and No 7 plate respectively

U6 U5 U4 U3 U2 U1

PCIP14

P6

P1

Figure 6 Layout of monitoring faces on the surface of SESB

3675m

Grid-destroying boundary

Grid-creating boundary

Interface

High-speed trains

Figure 5 Dynamic layering region


312 Train in Field Test e field test was carried out with ahigh-speed passing train of CRH380 Be speed of the trainpassing through the test section is relatively stablee train-induced vibration of the SESB is more intensive when thetrain speed is high enough

313 Data Recording System INV3060S dynamic data ac-quisition instrument was adopted to collect the vibrationinformation and the sampling frequency was 256 kHzMore than 20 sets of data were monitored on the open side

and the closed side among which 7 sets are about passingtrain speed around 330 kmh on near-line Preliminaryanalysis is carried out to eliminate abnormal data before dataprocessing and then statistical average is made on the 7 setsof valid data

32 Testing Results

321 Measured Results in Time Domain Now that thefrequency components of fluctuating pressure are differentfrom wheelrail interaction the measured vibration signalscould be processed by 20Hz low-pass filtering to obtain low-frequency vibration induced by the pressure Figure 9manifests the filtered results at monitoring points V1ndashV5on the SESB in time domain

e pressure-induced vibration of all measuring pointsV1ndashV5 on the closed side of the SESB is shown inFigures 9(a)ndash9(d) It indicates that all the waveforms showthe similar characteristics with the train-induced pulse ForV2 on the bottom the vibration response is relatively lessthan V1 and measured peak accelerations of V1 and V2are 25ms2 and 07ms2 respectively As shownin Figures 9(c)ndash9(d) the peak accelerations are 26ms222ms2 and 16ms2 for V3 V4 and V5 respectively evibration on the upper part (V1 and V3) is larger

322 Measured Results in Frequency Domain e mea-sured results from the field test in Figure 9 are transformedinto the frequency domain Because the fluctuating pressure

(a)

+1000e + 00+9160e ndash 01+8320e ndash 01+7480e ndash 01+6640e ndash 01+5800e ndash 01+4960e ndash 01+4120e ndash 01+3280e ndash 01+2440e ndash 01+1600e ndash 01+7597e ndash 01ndash8036e ndash 03

U U1

Y XZ

(b)

+1629e ndash 02+1473e ndash 02+1317e ndash 02+1161e ndash 02+1005e ndash 02+8434e ndash 03+6922e ndash 03+5360e ndash 03+3798e ndash 03+7236e ndash 03+6739e ndash 04ndash8881e ndash 04ndash2450e ndash 03

U U3

Y

Z

(c)

Figure 7 FEmodel of the SESB and typical modal vibration shape (a) finite elementmodel (b) the first transverse bending (400Hz) (c) thefirst vertical bending (545Hz)

Table 1 Material properties of SESB

Material E (Nm2) Poissonratio

Density(kgm3)

Dampingratio

Steel 206times1011 03 7850 0010Concrete 325times1010 02 2400 0030PC 232times109 04 1200 0200Aluminum 72times1010 03 2670 0010

Table 2 e first 10 modes of natural frequencies

Mode Frequency (Hz) Mode Frequency (Hz)1st 325 6th 4562ed 374 7th 4633th 400 8th 4684th 427 9th 4715th 446 10th 475


(a)

V1

V2

V5

V3

V4

Openside

Closedside

Accelerometer

2500

2500

2450

500

500

500

500

500

500

500

650

450

450

450

450

450

450

1100

(b)

Figure 8 Arrangement of accelerometer (a) photo of accelerometer arranging (b) accelerometer distribution on the SESB

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(a)

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

ndash10

ndash05

00

05

10

(b)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(c)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(d)

Figure 9 Measured acceleration time histories of SESB (a) V1 (b) V2 (c) V3 (d) V5


mainly acts within low-frequency range Figure 10 onlyshows the acceleration spectra below 20Hz It is indicatedthat the recorded peak acceleration induced by the pressureis about 078ms2 at 68Hz when the train is on the near-lineand is about 061ms2 at 33Hz when the train is on the far-line Compared to the calculated natural frequency exhibitedin Table 2 the frequency components of the SESB under thefluctuating pressure are different from the transverse modeat 4Hz although many small peaks appear in the acceler-ation spectra It can be inferred that the SESB could notresonate with the train-induced pressure Further investi-gation should be invested for fatigue issues of the SESBcombined with the pressure-induced strains but these issuesare not discussed in this article

e vibration acceleration from perceptible acceleration(about 10minus3ms2) to intolerable acceleration (about 103ms2)for the human body changes up to 1 million times evibration acceleration level (VAL) is hence adopted to judgethe vibration intensity of the SESB according to Chineserailway industry standard measurement of railway envi-ronmental vibration (TBT 3152ndash2007) and it could becalculated by the following formula

VAL 20lgarms

aref1113888 1113889 (1)

where VAL is vibration acceleration level arms is the virtualvalue of acceleration (ms2) and aref 10minus 6 ms2 is refer-ence acceleration In addition

arms

1T

1113946T

0a2(t)dt

1113971

(2)

whereT is analysis time and a(t) is vibration acceleration at ttime

e vibration is also presented by the way of one-thirdoctave spectra to show the overall trends in the frequencydomain because there are many peaks with different fre-quency components in the spectra as shown in Figure 10some of which cannot be reproduced through the simplifiednumerical calculation and the vibration trend of eachmeasuring point is not easy to distinguish Figure 11 il-lustrates the measured VAL spectra curves of measuringpoints V1simV5 from 1sim20Hz by one-third octave spectraFor V1 V3 V4 and V5 on upper and middle parts of SESBtheir vibration characteristics are similar to each other withdominant frequency range of 25 sim 5Hz is is due to theaction of fluctuating wind and the vibration characteristicsof sound barrier While for V2 located at barrierrsquos lowestpart its vibration peak is relatively smaller and occurred atthe frequency band of 10sim20Hz where low-frequencywheelrail interactions gradually become the main excita-tions of vibration However the pressure action is stilldominant within frequency range of 25sim5Hz

4 Validation Study

Firstly the CFD numerical method in this paper is verifiedby the fluctuating wind pressure on the surface of thesemicovered snow barrier along the high-speed railway line

generated by train traffic in reference [29] e corre-sponding model is established by using the same modellingmethod and parameter values in Section 22 of this papere comparison between the measured results and thesimulation ones at the speed of 252 km h is shown inFigure 12 It can be seen that the time history law of thesimulated pressure is consistent with the measured one eldquohead waverdquo generates when the head carriage passesthrough the measurement section and the ldquowake waverdquogenerates when the tail carriage passes e peak pressure ofwake wave is about 50ndash80 of that of head wave e peakvalue of head wave negative pressure and tail wave positivepressure obtained by numerical simulation is slightly largerthan the measured value mainly due to the vehicle modelwhich is Japanese high-speed train and different fromCRH380 B e simulated results are essentially in agree-ment with the measured ones so that the CFD model in this

V1V2V3

V4V5

2 4 6 8 10 12 14 16 18 200Frequency (Hz)

Acc

eler

atio

n (m

s2 )

00

02

04

06

08

10

Figure 10 Spectra of measurement acceleration

V1V2V3

V4V5

2 315 5 8 125 2012513 octave band frequency range (Hz)

70

80

90

100

110

120V

ibra

tion

acce

lera

tion

leve

l (dB

)

Figure 11 Measured vibration acceleration level spectrum ofSESB


paper can accurately simulate the fluctuating wind pressurecaused by the passing trains

e dynamic displacement from FE results introduced inSection 23 is transformed into the dynamic acceleration intime domain by second derivative and then the dynamicacceleration in frequency domain is formed by fast Fouriertransform Finally the VALs in 13 octave frequency bandare calculated according to formula (1) and (2) To validatethe accuracy of numerical models the processed simulatedresults are compared with the measured vibration acceler-ation in time domain and the VALs in frequency domain

Figure 13 compares the simulated and filtered measuredvibration acceleration in time domain of measuring pointsV1 and V2 on the enclosed side e simulated accelerationsare in accordance with measured ones and the waveforms ofboth curves are consistent with the train-induced fluctuatingpressure However the measured accelerations especiallyfor the lowest measuring point V2 have some higher fre-quency components when the intermediate section of a trainpassing by is may be both due to the wheel-rail inter-actions the lower parts of SESB suffer more below 20Hz anddue to the aerodynamic force induced by the intercarriagediscontinuities in low-frequency which cannot be repro-duced by the CFD model e maximum vibrations of theSESB in low-frequency component are caused by the headand tail pulse of fluctuating pressure and the vibration timehistory obtained by filtering can reflect the dynamic char-acteristics of the fluctuating wind which ensure that the20Hz low-pass filtering is effective enough in reflecting thepressure-induced vibration

Figure 14 exhibits the one-third octave of VAL ofmeasuring points V1 and V2 (enclosed side) and V3 and V5(open side) derived from the numerical models and filteredmeasured results It can be seen that the simulated char-acteristics of all points are consistent with the measured onesin 1sim10Hz frequency range with peak value at 4Hz and themeasured results are slightly larger than the simulated onesdue to the remained low-frequency wheelrail forces In

10sim20Hz frequency range the simulated results are not thatconsistent with the measured ones is is because the train-induced pressure attenuates in this frequency range and thewheelrail forces gradually become the main excitations forthe vibration of the SESB

It can also be proved that the vibration accelerations onthe open side are consistent with the measured results(V3ndashV5) in time domain and frequency domain So far itcan be concluded from above comparison that the fluctu-ating pressure is the main excitation of vibration in fre-quency range 1sim20Hz Both the calculated acceleration timehistories and the VAL spectra of vibration are in accordancewith the measured ones and it is not worth bothering to takewheelrail forces into account when analyzing the charac-teristics of vibration under pressure erefore the presentnumerical models are able to reproduce the fluctuatingpressure and the resultant dynamic response of the SESBwith sufficient accuracy and are can be used for furtherdiscussions

5 Discussion

Based on the calibrated CFD and FE models of aerodynamicpressure and vibration of SESB the characteristics ofaerodynamic pressure and dynamic response under differentfactors are investigated in this section Two influentialfactors operation line and number of top SIP are discussedTrain speed is uniformly set as 350 kmh for parameterstudies In order to generalize the results the responsequantities in the following test including the time and thefluctuating pressure are dimensionless using the train ve-locity according to the following formulas

T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)

where t is the measured time from the passage of the nose ofthe train with length L P(T) is the calculated pressure P0 isthe undisturbed atmospheric pressure and ρ is the density ofair

51 Effect ofOperating Line e pressure distribution on theinner surface and the vibration law of the steel frame of theSESB are discussed All the monitoring points are shown inFigure 15 among which O1simO4 C1simC4 are on the steelstuds of the open and closed sides andD1simD5 are on the topcrossbeam e adjacent point intervals on the same side areall 25m

511 Near-Line Figure 16 describes the dimensionlesspressure and acceleration under dimensionless time whenthe train is running on the near-line In this part the analysisfocuses on the head pulse and tail pulse that produce themaximum vibrations of the SESB It can be seen fromFigures 16(a) and 16(b) that the peak pressure coefficient Cpof positive pressure of head pulse is the largest at C3ndashC4 at

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10

Measured pressureSimulated pressure

Figure 12 Comparisons of the simulated train-induced fluctuatingpressure


the bottom of the closed side of the SESB which is 0137 atC4 and decreases rapidly in the closed side from C3 to 0071at C1 At the top of the SESB the pressure coefficient is only13 compared to that of C4 on the bottom of the closed sideand decreases linearly from 0062 at D5 to 0041 at D3 eCP of the negative peak of head pulse and positive andnegative peaks of tail pulse are in the similar cases

e pressure-induced vibrations at typical location onthe steel frame of the SESB are presented in Figures 16(c)ndash16(e) It is obvious that the large vibration of the SESB ismainly triggered both by the head and tail pulse of thepressure When each pulse reaches to the first small peakvalue the vibrations start to increase when each pulsereaches to the second peak the vibration reaches to the firstpeak e head pulse excites the vibration of the SESB toarrive at the positive acceleration peak and the tail pulsecauses the negative acceleration peak e absolute value ofthe former is greater than that of the latter because the peakpressure of the head pulse is greater than that of the tailpulse e vibration always lags the pulses and the maxi-mum vibration happens with the disappearance of thepulses en the SESB periodically attenuates and the at-tenuation period of the vibration on top crossbeam is fasterthan that of the bilateral steel studs e vibration is notproportional to the fluctuating pressure and the largestvibrations on both sides of the SESB appear at C1 and O1which have the smallest pressure coefficient and decreasegradually from top part to the bottom part of the steel studsDue to the connectivity of top crossbeam the vibration lawon the closed side is similar to that on the open side egreatest vibration of the top crossbeam locates in the middleD3 point and decreases gradually from D3 in the middle toboth ends of the crossbeam

In order to compare the vibration among all monitoredpoints on SESB Figure 17 exhibits the peak accelerationsand the overall VAL on all points It can be seen that thedistribution of accelerations and VAL are basically the samee peak vibration acceleration is about 23ms2 on bothsides and the top of the SESB which indicates that the soundbarrier moves as a whole under the action of fluctuatingpressure As can be seen for O1 and C1 points on steel studstop the overall VAL is 115 dB For measuring points O2simO4and C2simC4 vibrations on the upper points are larger thanthose of lower ones and vibrations on the closed side arelarger than those on the open side It is because the bottompoint is close to the fixed end and is subject to greaterconstraints while the upper point is far away from therestraint end For D1simD5 on top crossbeam vibration ofmeasuring point D3 at midspan is the most violent with theoverall VAL of 112 dB Although much lower pressureloading on the top of SESB D3 point has smaller constraintsbut subjected to larger dynamic bending moments

V1 measuredV1 simulated

Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)

Figure 13 Comparisons of the simulated acceleration time histories with the measured ones

V1 simulatedV1 measured

V2 simulated V2 measured

60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)


Figure 14 Comparisons of the simulated VALs with measuredones

O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5

Figure 15 Layout of the monitoring points for parameter analysis


C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

07 08 09 10 11 12ndash015ndash010ndash005

000005010015

C P

ndash015ndash010ndash005

000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)

07 08 09 10 11 12Dimensionless time T

Dimensionless time T Dimensionless time T

O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


ndash02 ndash01 00 01

(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

Figure 16 Time histories of the pressure coefficients and peak acceleration under dimensionless time when train on the near-line (a) headpulse (b) tail pulse (c) peak acceleration on the closed side (d) peak acceleration on the open side and (e) peak acceleration on the topcrossbeam


Vibrations of D4 and D5 are slightly larger than D2 and D1because the former two points are loaded larger pressurethan the latter two points

512 Far-Line e dimensionless pressure on the innersurface of the closed side and vibrations during the trainrunning on far-line are shown in Figure 18 e peak pressurecoefficient as described in Figures 18(a) and 18(b) is 0033 atC1 which is only 14 of the value when the train is running onthe near-line and the pressure distributes almost uniformlywhen the train is on the far-line Under the action of smallerpressure the peak vibrations still lag the occurrence of the headand the tail pulse and the SESB still undergoes periodic at-tenuation vibration e vibration periods of both sides areconsistent and larger than that of the top crossbeam

e peak acceleration and overall VAL of the SESBduring the far-line operation are illustrated in the Figure 19and it can be seen that the vibration acceleration and overallVAL in far-line case are far less than those in the near-linecase Although the vibration on both sides is the samevibrations on the top are greater while the bottom one is lessbut the vibration acceleration and total VAL of each mea-suring point on the open side are greater than those on thesymmetrical position on the closed side It can be seen thatfor the measuring points O1 on the top of steel studs on theopen side the peak acceleration is 08ms2 and the overallVAL is 105 dB Also for measuring points O2simO4 andC2simC4 vibration on the same height are similar to eachother and vibrations of upper points are larger than those oflower ones For the vibration of top crossbeam the mea-suring point D3 located at midspan has the largest vibrationwith 11ms2 peak acceleration and the overall VAL of108 dB compared to other points on the crossbeam and eventhe upper measuring C1 and O1 on studs

52 Effect of Top Plates e main difference between theSESB and conventional upright sound barrier is whether ornot the top of the sound barrier is closedere are top plates

on the SESB To systematically explore the length effect oftop plates on fluctuating pressure and its induced vibrationof SESB seven numerical cases including sound barrierswithout any top plates (equivalent to uptight barrier) withonly one top corner curve plate with one top corner curveplate following 1sim5 top plates (104m wide for each plate)are built and discussed under 350 kmh high-speed trainoperating on the near-line

521 Fluctuating Pressure After calculation the CP perdimensionless time in different cases is similar toFigures 16(a) and 16(b) According to the calculated resultsfor all cases with or without the top plates the greatestfluctuating pressure is still located at the lower part of thesteel studse peak pressure increases with the extension ofthe length of total top plates and the increment in themagnitude of Cp is 00013m for the peak positive pressuremainly loading at the lower part (C1ndashC2) and 00014m forthe peak negative pressure appearing at higher position(plates PC2ndashC3) e pressures on the C1 C2 and C4 pointswere chosen to be analyzed Table 3 tabulates the peakpositive and negative Cp on the three points under each caseAs can be seen with the extension length ranging from1ndash3m Cp enlarges severely While with the extension lengthrange of 3ndash5m the pressure has small increases

Without any top plates the peak pressure loading on C4is approximately 25 times larger than that loading on C1with peak CP of 0138 and -0053 respectively Compared topressure of SESB with 6 top plates added to 1 corner curveplate peak CP on C4 and C1 weakens by about 001 and0025 respectively ie the reduction rates are 7 and 32All the top plates of the SESB mitigate the attenuation rate offluctuating pressure which makes the SESB subject togreater fluctuating wind pressure

In all the top plates confine the size of air circulating areawhen calculating the fluctuating pressure which in turnenlarges the pressure on the inner surface of the barrier andthe pressure acting on the SESB is more likely to be enlargedwith the increasing extension length of top plates

0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )

O1 O2 O3 O4 C1 C2 C3 C4 D1 D2 D3 D4 D5Measuring point number

(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)

Figure 17 Vibration of SESB (a) peak acceleration on the steel frame (b) overall vibration acceleration level on the steel frame


ndash02 ndash01 00 01 02 03 04 07 08 09 10 11 12ndash0036

ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

Figure 18 Time histories of the pressure coefficients and peak acceleration under dimensionless time when train on the far-line (a) headpulse (b) tail pulse (c) peak acceleration on the closed side (d) peak acceleration on the open side and (e) peak acceleration on the topcrossbeam


Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)


Table 3 Peak CP on monitored section of SESB

Working condition Peak positive CP on C4 Peak negative CP on C2 Peak negative CP on C1No top plates 0138 minus0115 minus0053Only curve plate 0140 minus0116 minus00541 top plate 0141 minus0117 minus00612 top plates 0143 minus0119 minus00683 top plates 0144 minus0121 minus007124 top plates 0145 minus0122 minus007385 top plates 0146 minus0124 minus00759

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)

Figure 20 Vibration of SESB with different numbers of top plates (a) peak acceleration of the steel frame (b) overall vibration accelerationlevel of the steel frame


522 Vibration of SESB To discuss the influence of the topplates on the vibration of SESB the vibration distributions ofabove seven cases are shown in Figure 20 As can be seenwhen there are no top plates the peak vibration accelerationof O1 is 23ms2 larger than that of C1 about 21ms2 Asfor the overall VAL there are little difference between O1andC1 because the top crossbeam can effectively connect theopen side and closed side of steel studs Vibrations of the topcrossbeam (D1simD5) are relatively smaller compared to theupper parts of steel studs is is because there is noaerodynamic pressure loading on the barrier top

For the case with one curve plate and one top platecompared to the case without top plates the peak acceler-ation on O1 is 15ms2 attenuates quickly by 35 is isbecause the curve plate and the top plate work as connec-tions connecting adjacent steel frames to the target steelframe and therefore dissipated the vibration e overallVAL of O1 and C1 is still consistent for the good connec-tivity of top cross beam

As for the cases with different numbers of top plates thetrain-induced pressure is magnified with the plate numberincreasing from 1 to 5 which in turn enlarges the dynamicresponse of the barriere peak acceleration ofO1 andC1 perunit extending length of top plates is 017 (ms2) and 012 (ms2) respectively For the pointD3 at themidspan of crossbeamthe increasing rate of peak vibration is 017 (ms2)m eincrease rate of the overall VAL for measuring points O1 C1and D3 is about 05 dBm which are consistent with eachother

In all top plates have significant influences on dynamicresponse under fluctuating pressure loading on SESB epressure-induced vibration at the top of both steel studs and themiddle of the crossbeam of SESB is the largest and increaseswith the increase of the number of top plates erefore inaddition to paying attention to the noise reduction character-istics of SESBs it is also necessary to prevent the engineeringproblems that may be caused by the high-speed train-inducedvibration on the upper and top parts

6 Conclusions

In this paper vibration of the SESB is firstly measured in a insitu test and verified by numerical simulation A series ofstudies are then carried out on the dimensionless time andconclusions could be drawn as follows

(1) To distinguish the vibration under the fluctuatingpressure from original vibration signals accordingthe frequency component of aerodynamic loads theeffect of wheelrail forces on vibration responses ofthe SESB could be neglected when analyzing thecharacteristics of vibration under aerodynamicpressure

(2) After model calibration through the in-site field testthe presented numerical models are able to reproducethe fluctuating pressure and pressure-induced dynamicresponses of the SESB with sufficient accuracy

(3) When the train is running on the near-line thelargest pressure coefficient is on the bottom part of

the closed side of the SESB and decreases graduallywith the height of the steel stud and pressure on topcrossbeam also decreases from the closed side to theopen side

(4) Under the action of the head pulse and tail pulse ofthe fluctuating pressure the vibration lagging behindwill occur and will be periodically attenuated evibration laws on both sides of the SESB are thesame

(4) e pressure-induced vibration is the largest on thetop of the steel studs and in the middle of crossbeamand the smallest at the bottom of steel studs

(5) Top plates have great influences on the fluctuatingpressure and the corresponding vibration elonger is the total length of the top plates the greaterare the pressure and vibration on the inner surface

Data Availability

e data used to support the findings of this study are in-cluded within the article and available from the corre-sponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was funded by the National Natural ScienceFoundation of China (grant no 51878565) and the KeyProjects of Chongqing Application and Development Plan(no cstc2014yykfB30003)

References

[1] X Zhang W Zhai Z Chen and J Yang ldquoCharacteristic andmechanism of structural acoustic radiation for box girderbridge in urban rail transitrdquo Science of the Total Environmentvol 627 pp 1303ndash1314 2018

[2] Q Li and D J ompson ldquoPrediction of rail and bridge noisearising from concrete railway viaducts by using a multilayerrail fastener model and a wavenumber domain methodrdquoProceedings of the Institution of Mechanical Engineers Part FJournal of Rail and Rapid Transit vol 232 no 5 pp 1326ndash1346 2018

[3] L Song X Li H Hao and X Zhang ldquoMedium- and high-frequency vibration characteristics of a box-girder by thewaveguide finite element methodrdquo International Journal ofStructural Stability and Dynamics vol 18 no 11 Article ID1850141 2018

[4] N Zhang Y Tian and H Xia ldquoA train-bridge dynamicinteraction analysis method and its experimental validationrdquoEngineering vol 2 no 4 pp 528ndash536 2016

[5] Q Li X Song and DWu ldquoA 25-dimensional method for theprediction of structure-borne low-frequency noise fromconcrete rail transit bridgesrdquo -e Journal of the AcousticalSociety of America vol 135 no 5 pp 2718ndash2726 2014

[6] D J ompson Railway Noise and Vibration MechanismsModeling and Means of Control Elsevier Oxford UK 2008


[7] H M Lee Z M Wang K M Lim and H P Lee ldquoInves-tigation of the effects of sample size on sound absorptionperformance of noise barrierrdquo Applied Acoustics vol 157Article ID 106989 2020

[8] X Zhang R Liu Z Cao X Wang and X Li ldquoAcousticperformance of a semi-closed noise barrier installed on ahigh-speed railway bridge measurement and analysis con-sidering actual service conditionsrdquo Measurement vol 138pp 386ndash399 2019

[9] P A Morgan D C Hothersall and S N Chandler-WildeldquoInfluence of shape and absorbing surface-a numerical studyof railway noise barriersrdquo Journal of Sound and Vibrationvol 217 no 3 pp 405ndash417 1998

[10] T Ishizuka and K Fujiwara ldquoPerformance of noise barrierswith various edge shapes and acoustical conditionsrdquo AppliedAcoustics vol 65 no 2 pp 125ndash141 2004

[11] S I Voropayev N C Ovenden H J S Fernando andP R Donovan ldquoFinding optimal geometries for noise barriertops using scaled experimentsrdquo -e Journal of the AcousticalSociety of America vol 141 no 2 pp 722ndash736 2017

[12] Z Wang L K Meng P Pracheu and L H Pueh ldquoAppli-cations of noise barriers with a slanted flat-tip jagged canti-lever for noise attenuation on a construction siterdquo Journal ofVibration and Control vol 24 no 22 pp 5225ndash5232 2018

[13] M Tokunaga M Sogabe and K Ono ldquoDynamic responseevaluation of tall noise barrier on high speed railway struc-turesrdquo Journal of Sound and Vibration vol 366 pp 293ndash3082016

[14] X-Z Santo X-H Liu D-J Liu and X Zhang ldquoInfluences ofsoil-structure interaction on coupled vibration of train-bridgesystem theoretical and experimental studyrdquo Advances inStructural Engineering vol 16 no 8 pp 1355ndash1364 2013

[15] T X Wu and D J ompson ldquoVibration analysis of railwaytrack with multiple wheels on the railrdquo Journal of Sound andVibration vol 239 no 1 pp 69ndash97 2001

[16] Q Li K Wang S Cheng W Li and X D Song ldquoVibrationanalysis of concrete bridges during a train pass-by usingvarious modelsrdquo Journal of Physics Conference Seriesvol 744 Article ID 012140 2016

[17] N Zhang and H Xia ldquoDynamic analysis of coupled vehicle-bridge system based on inter-system iteration methodrdquoComputers amp Structures vol 114-115 pp 26ndash34 2013

[18] L Liang X Li J Yin D Wang W Gao and Z Guo ldquoVi-bration characteristics of damping pad floating slab on thelong-span steel truss cable-stayed bridge in urban rail transitrdquoEngineering Structures vol 191 pp 92ndash103 2019

[19] X Song and Q Li ldquoNumerical and experimental study onnoise reduction of concrete LRT bridgesrdquo Science of -e TotalEnvironment vol 643 pp 208ndash224 2018

[20] J R Bell D Burton M C ompson A H Herbst andJ Sheridan ldquoMoving model analysis of the slipstream andwake of a high-speed trainrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 136 pp 127ndash137 2015

[21] Z Chen T Liu X Zhou and J Niu ldquoImpact of ambient windon aerodynamic performance when two trains intersect insidea tunnelrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 169 pp 139ndash156 2017

[22] D Soper C Baker A Jackson et al ldquoFull scale measurementsof train underbody flows and track forcesrdquo Journal of WindEngineering and Industrial Aerodynamics vol 169 pp 251ndash264 2017

[23] C Baker ldquoe flow around high-speed trainsrdquo Journal ofWind Engineering and Industrial Aerodynamics vol 98 no 6-7 pp 277ndash298 2010

[24] N Yang X-K Zheng J Zhang S S Law and Q-S YangldquoExperimental and numerical studies on aerodynamic loadson an overhead bridge due to passage of high-speed trainrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 140 pp 19ndash33 2015

[25] M Lu Q Li Z Ning and Z Ji ldquoStudy on the aerodynamicload characteristic of noise reduction barrier on high-speedrailwayrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 176 pp 254ndash262 2018

[26] L Carassale and M Marre Brunenghi ldquoDynamic response oftrackside structures due to the aerodynamic effects producedby passing trainsrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 123 pp 317ndash324 2013

[27] W J Luo and H B Li ldquoDynamic response analysis of noisebarrier structures under impulsive wind loadrdquo Noise andVibration Control vol 36 no 2 pp 162ndash165 2016

[28] T Zhang H Xia and W Guo ldquoAnalysis on running safety oftrain on the bridge considering sudden change of wind loadcaused by wind barriersrdquo Frontiers of Structural and CivilEngineering vol 12 no 4 pp 558ndash567 2018

[29] A Horie and T Sugiyama ldquoField test of train draft on TohokuShinkansenrdquo Technical Report A-86 Railway Technical Re-search pre-Report Tokyo Japan 1986


method For recommending the most suitable model infurther prediction Li et al [16] compared the computationcost and accuracy of results obtained from the mode su-perposition method in the time domain and power flowmodels for the vehicle-rail-bridge coupled system areestablished in the frequency domain Zhang and Xia [17]conducted dynamic analysis of the coupled vehicle-bridgesystem based on the intersystem iteration method esemethods all above are often applied in the vibration andvibroacoustic analysis of the coupled system When soundbarriers installed on bridges these methods are still appli-cable Li and Liang [18] investigated the influence of dif-ferent track structures on the vibration and structure-bornenoise of elevated concrete box girders with the frequency-domain theoretical model of the vehicle-track coupledsystem Song and Li [19] compared the effects of three noisemitigation measures on noise control installation of a noisebarrier use of a rail pad with a lower stiffness and adoptingof a floating ladder track With the train speeding upaerodynamic action and its resultant vibration of soundbarrier cannot be ignored Many related research studiesincluding basic studies aiming at the qualitative descriptionof the pressure fluctuation frequency-domain distributionof fluctuating wind and pressure-induced vibration re-sponse have been carried out e general rules of fluctu-ating wind pressure versus time and its related factors wereexplored through scale measurements in situ tests andnumerical simulations [20ndash23] Consistent conclusionsyielded from these studies are that the pressure time historycurve includes the head pulse with a positive peak followedby a asymmetric negative peak appearing at the headstockpassage the small amplitude pressure fluctuation caused bythe intercarriage gaps and the tail pulse with a negative and apositive amplitude as a sequence of the tailstock passageepeak pressure is related to train speed vehicle type anddistance from sound barrier to the train Yang et al [24]decomposed the fluctuating pressure signal collected in afield test targeting at a sound barrier in different frequencybands and figured out that the surface pressure componentin frequency band (0ndash25Hz) is large while that in higherfrequency band (5ndash10Hz) is relatively small Lu et al [25]figured out that the frequency component of the aerody-namic load is less than 10Hz Carassale and Marre Bru-nenghi [26] carried out an open-air experiment to separatethe dynamic response of the aerodynamic forces on atrackside steel frame from the effect of the seismic actioncaused by the train transit According to Carassale the headpulse and the tail pulse on the frequency map have a peakfrequency of about 58Hz Luo and Zhang and Xia [27 28]derived the calculation formulas for change of wind loadacting on the car-body for a l0-span simply supportedU-shaped girder bridge with 100m long double-side 35mbarrier and analyzed the influence of sudden change of windload on the running safety of the train when a train movesinto or out of the wind barrier structure

Most of mentioned studies are aimed at some othertrackside structures or sound barriers with simple structuressuch as vertical sound barriers or simple barriers with lowheight whereas for semienclosed sound barriers (SESBs)

with complicated structure the train-induced fluctuatingpressure and its resultant dynamic response have not beenwell studied

is paper aims to bridge this gap by describing theprocedures of a battery of experimental and numerical in-vestigations carried out on a SESB arranged on a high-speedrailway bridge Firstly train-induced fluctuating pressureand its consequent vibration were simulated numericallyand then the vibration test of SESB is introduced esimulated results were compared with the processed mea-sured results for model validation e verified models werefinally applied to carry out parameter studies to investigateand discuss the influences of operating lines and total lengthof top unit plates on the aerodynamic pressure and dynamicresponse of the barrier e results are of major importanceand subsequently be used (1) to extract the pressure-inducedvibration from original vibration signals according to thefrequency component of fluctuating pressure (2) to obtainthe distribution law of fluctuating pressure at different lo-cations of the SESB under different factors and (3) to derivea fundamental understanding of the vibration responseinduced by fluctuating pressure of high-speed passing trains

e composition of the SESB the CFD model for train-induced fluctuating pressure and the FEmodel for pressure-induced vibration were built respectively in Section 2 esetup of vibration test and main experimental results wereset out in Section 3 en in Section 4 the CFD and FEnumerical models were verified Parameter studies werefinally carried out in Section 5 to discuss the characteristicsof fluctuating pressure and resultant dynamic response ofthe SESB

2 Calculating Models

21-e Semienclosed SoundBarrier e target SESB is fixedon the flanges of the 326m long dual-track simply sup-ported box-girder viaduct of the Hang Zhou-Changshapassenger dedicated line China e cross section of thebarrier and the bridge girder below it are illustrated inFigure 1 e SESB is 815m in height 117m in width and15 km in length and its main structures with 2m intervalswere steel frames composed of bilateral erect steel studs andtop crossbeams To improve the stability of the steel frameslongitudinal bracings are arranged at different heights alongthe longitudinal direction e main noise reduction com-ponents of the SESB are the metal sound insulation platesand transparent PC plates installed on the barrier e steelstuds and crossbeams are H-shaped steel with a dimensionof 300mmtimes 300mmtimes 10mmtimes 15mm Metal plates on theclosed side of the SESB as shown in Figure 2 are 0140mthick and 045m or 05m wide and the PC ones are 002mthick and 11m wide on the side and 104m wide on the topA total of 14 plates are inserted between the flange of H-typeerect steel studs and stuffed rubber into interstices betweenthe plates and the flange of H-type studs On the top cornerof SESB a curved PC plate with 099m radius was installedere are 6 PC plates arranged between every two adjacentcrossbeams For further discussion the track near theenclosed side of barrier is defined as the near-line and on the



22 CFD Model




Open

Side

Box girder


Closed


Crossbeams

Eract steel studs

Metal plates

PC plates


Near line Far line

11700

990 3480 104010401040 1040 10401040 990

8150

(a)

2000 2000 2000 2000

(b)

2000 2000 2000 2000

1170

090

010

4010

4010

4010

4010

4010

4034

8099

0

(c)






761m

247m257m

(a)

Bridge deck

815

m

117m

389

m

025

m

326m

624m


(b)


1681m

3675m87

7m

Y

X Z









U6 U5 U4 U3 U2 U1

PCIP14

P6

P1


3675m



Interface

High-speed trains






32 Testing Results




(a)


U U1

Y XZ

(b)


U U3

Y

Z

(c)




Density(kgm3)

Dampingratio





(a)

V1

V2

V5

V3

V4

Openside

Closedside

Accelerometer

2500

2500

2450

500

500

500

500

500

500

500

650

450

450

450

450

450

450

1100

(b)


ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(a)

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

ndash10

ndash05

00

05

10

(b)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(c)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(d)





VAL 20lgarms

aref1113888 1113889 (1)


arms

1T

1113946T

0a2(t)dt

1113971

(2)



4 Validation Study



V1V2V3

V4V5

2 4 6 8 10 12 14 16 18 200Frequency (Hz)

Acc

eler

atio

n (m

s2 )

00

02

04

06

08

10


V1V2V3

V4V5


70

80

90

100

110

120V

ibra

tion

acce

lera

tion

leve

l (dB

)









5 Discussion


T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)




400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10








Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References

































22 CFD Model




Open

Side

Box girder


Closed


Crossbeams

Eract steel studs

Metal plates

PC plates


Near line Far line

11700

990 3480 104010401040 1040 10401040 990

8150

(a)

2000 2000 2000 2000

(b)

2000 2000 2000 2000

1170

090

010

4010

4010

4010

4010

4010

4034

8099

0

(c)






761m

247m257m

(a)

Bridge deck

815

m

117m

389

m

025

m

326m

624m


(b)


1681m

3675m87

7m

Y

X Z









U6 U5 U4 U3 U2 U1

PCIP14

P6

P1


3675m



Interface

High-speed trains






32 Testing Results




(a)


U U1

Y XZ

(b)


U U3

Y

Z

(c)




Density(kgm3)

Dampingratio





(a)

V1

V2

V5

V3

V4

Openside

Closedside

Accelerometer

2500

2500

2450

500

500

500

500

500

500

500

650

450

450

450

450

450

450

1100

(b)


ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(a)

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

ndash10

ndash05

00

05

10

(b)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(c)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(d)





VAL 20lgarms

aref1113888 1113889 (1)


arms

1T

1113946T

0a2(t)dt

1113971

(2)



4 Validation Study



V1V2V3

V4V5

2 4 6 8 10 12 14 16 18 200Frequency (Hz)

Acc

eler

atio

n (m

s2 )

00

02

04

06

08

10


V1V2V3

V4V5


70

80

90

100

110

120V

ibra

tion

acce

lera

tion

leve

l (dB

)









5 Discussion


T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)




400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10








Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References



































761m

247m257m

(a)

Bridge deck

815

m

117m

389

m

025

m

326m

624m


(b)


1681m

3675m87

7m

Y

X Z









U6 U5 U4 U3 U2 U1

PCIP14

P6

P1


3675m



Interface

High-speed trains






32 Testing Results




(a)


U U1

Y XZ

(b)


U U3

Y

Z

(c)




Density(kgm3)

Dampingratio





(a)

V1

V2

V5

V3

V4

Openside

Closedside

Accelerometer

2500

2500

2450

500

500

500

500

500

500

500

650

450

450

450

450

450

450

1100

(b)


ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(a)

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

ndash10

ndash05

00

05

10

(b)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(c)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(d)





VAL 20lgarms

aref1113888 1113889 (1)


arms

1T

1113946T

0a2(t)dt

1113971

(2)



4 Validation Study



V1V2V3

V4V5

2 4 6 8 10 12 14 16 18 200Frequency (Hz)

Acc

eler

atio

n (m

s2 )

00

02

04

06

08

10


V1V2V3

V4V5


70

80

90

100

110

120V

ibra

tion

acce

lera

tion

leve

l (dB

)









5 Discussion


T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)




400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10








Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References






































U6 U5 U4 U3 U2 U1

PCIP14

P6

P1


3675m



Interface

High-speed trains






32 Testing Results




(a)


U U1

Y XZ

(b)


U U3

Y

Z

(c)




Density(kgm3)

Dampingratio





(a)

V1

V2

V5

V3

V4

Openside

Closedside

Accelerometer

2500

2500

2450

500

500

500

500

500

500

500

650

450

450

450

450

450

450

1100

(b)


ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(a)

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

ndash10

ndash05

00

05

10

(b)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(c)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(d)





VAL 20lgarms

aref1113888 1113889 (1)


arms

1T

1113946T

0a2(t)dt

1113971

(2)



4 Validation Study



V1V2V3

V4V5

2 4 6 8 10 12 14 16 18 200Frequency (Hz)

Acc

eler

atio

n (m

s2 )

00

02

04

06

08

10


V1V2V3

V4V5


70

80

90

100

110

120V

ibra

tion

acce

lera

tion

leve

l (dB

)









5 Discussion


T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)




400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10








Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References



































32 Testing Results




(a)


U U1

Y XZ

(b)


U U3

Y

Z

(c)




Density(kgm3)

Dampingratio





(a)

V1

V2

V5

V3

V4

Openside

Closedside

Accelerometer

2500

2500

2450

500

500

500

500

500

500

500

650

450

450

450

450

450

450

1100

(b)


ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(a)

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

ndash10

ndash05

00

05

10

(b)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(c)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(d)





VAL 20lgarms

aref1113888 1113889 (1)


arms

1T

1113946T

0a2(t)dt

1113971

(2)



4 Validation Study



V1V2V3

V4V5

2 4 6 8 10 12 14 16 18 200Frequency (Hz)

Acc

eler

atio

n (m

s2 )

00

02

04

06

08

10


V1V2V3

V4V5


70

80

90

100

110

120V

ibra

tion

acce

lera

tion

leve

l (dB

)









5 Discussion


T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)




400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10








Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References
































(a)

V1

V2

V5

V3

V4

Openside

Closedside

Accelerometer

2500

2500

2450

500

500

500

500

500

500

500

650

450

450

450

450

450

450

1100

(b)


ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(a)

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

ndash10

ndash05

00

05

10

(b)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(c)

ndash3

ndash2

ndash1

0

1

2

3

0 1 2 3 4 5Time (s)

Acc

eler

atio

n (m

s2 )

(d)





VAL 20lgarms

aref1113888 1113889 (1)


arms

1T

1113946T

0a2(t)dt

1113971

(2)



4 Validation Study



V1V2V3

V4V5

2 4 6 8 10 12 14 16 18 200Frequency (Hz)

Acc

eler

atio

n (m

s2 )

00

02

04

06

08

10


V1V2V3

V4V5


70

80

90

100

110

120V

ibra

tion

acce

lera

tion

leve

l (dB

)









5 Discussion


T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)




400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10








Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References


































VAL 20lgarms

aref1113888 1113889 (1)


arms

1T

1113946T

0a2(t)dt

1113971

(2)



4 Validation Study



V1V2V3

V4V5

2 4 6 8 10 12 14 16 18 200Frequency (Hz)

Acc

eler

atio

n (m

s2 )

00

02

04

06

08

10


V1V2V3

V4V5


70

80

90

100

110

120V

ibra

tion

acce

lera

tion

leve

l (dB

)









5 Discussion


T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)




400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10








Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References






































5 Discussion


T tVtrain

L

CP P(T) minus P0

05ρV2train

(3)




400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Pres

sure

(Pa)

0 2 4Time (s)

6 8 10








Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References




































Acc

eler

atio

n (m

s2 )

ndash3

0

3

1 2 3 4 50Time (s)

(a)


Acc

eler

atio

n (m

s2 )

ndash1

0

1

1 2 3 4 50Time (s)

(b)




60

80

100

120

Vib

ratio

n ac

cele

ratio

n le

vel (

dB)



O4

O3

O2

O1

C4

C3

C2

C1

D1 D2 D3 D4 D5



C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References
































C1C2

C3C4

D5

C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5


000005010015

C P


000005010015

C P

ndash02 ndash01 00 01 02 03 04 05 06

(c)



O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)



(b)(a)

02 03 04

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns











0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References








































0

1

2

3Pe

ak ac

cele

ratio

n (m

s2 )


(a)


80

100

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

(b)




ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References

































ndash0024

ndash0012

0000

0012

0024

0036


C1C2

C3C4

ndash02 ndash01 00 01 02 03 04 05 06

(c)


O1O2

O3O4

ndash02 ndash01 00 01 02 03 04 05 06

(d)


D5D1D2D3

D4

ndash02 ndash01 00 01 02 03 04 05 06

(e)


C1C2C3C4

C1C2C3C4

D3D4D5

D3D4D5

(b)(a)

C P

ndash0036

ndash0024

ndash0012

0000

0012

0024

0036

C P

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns

ndash2

ndash1

0

1

2

Acc

eler

atio

ns



Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References
































Peak

acce

lera

tion

(ms

2 )

00

05

10

15


(a)

80

90

100

110

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)


(b)




No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates

00

05

10

15

20

25

Peak

acce

lera

tion

(ms

2 )


(a)

90

100

110

120

Tota

l vib

ratio

n ac

cele

ratio

n le

vel (

dB)

No top plates

Curve plate

1 top plate

2 top plates

3 top plates

4 top plates

5 top plates


(b)







6 Conclusions









Data Availability




Acknowledgments


References




































6 Conclusions









Data Availability




Acknowledgments


References
































train-inducedfluctuatingpressureandresultantdynamic...

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