A Prediction Method of Historical Timber Buildings’ Vibrations …downloads.hindawi.com/journals/sv/2017/1451483.pdf · Vibrations Induced by Traffic Loads and Its Validation YunshiZhang,NanZhang,YanmeiCao,andHeXia

Research ArticleA Prediction Method of Historical Timber BuildingsrsquoVibrations Induced by Traffic Loads and Its Validation

Yunshi Zhang Nan Zhang Yanmei Cao and He Xia

School of Civil Engineering Beijing Jiaotong University Beijing 100044 China

Correspondence should be addressed to Nan Zhang nzhangbjtueducn

Received 17 September 2016 Revised 7 December 2016 Accepted 13 December 2016 Published 7 March 2017

Academic Editor Vadim V Silberschmidt

Copyright copy 2017 Yunshi Zhang et al This 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

A prediction method in the frequency domain is proposed for predicting the vibrations of historical timber building inducedby traffic loads The modal parameters of a structure are identified using a double-confirmation analysis method based on theautospectrum Then the vibration responses of the building are calculated using a limited number of measurement records byinputting the calculated vibration information for the foundation of the updated building model The proposed method is used topredict the vibrations of the Buddhist sutra depositary at Yangzhou Zhunti Temple Comparing the results shows that the vibrationresponses of a structure under traffic loads can be effectively predicted in the relevant frequency bands

1 Introduction

Wooden structures played a vital role in Chinese archi-tectural history Wooden architecture is a treasure thatcombines structural form and architectural art and ancientChinese wooden architecture made excellent contributionsto promoting the development of historic timber buildingsHowever over time the reliability and bearing performanceof these wooden structures are constantly decreasing Theattenuation of the structural performance of historical timberbuilding is rapidly increasing with increased people loadsand surrounding traffic loads Consequently the vibrationprediction and evaluation of historical timber buildings sub-jected to ambient traffic loads are necessary so that vibrationisolationmeasures can be applied to limit the damage to thesebuildings and to extend their service life

Researchers have conducted many studies to analyzethe vibrations of historic buildings [1ndash22] The dynamiccharacteristics of structures have been measured using fieldtests based on the ambient vibration exactions [1 2 5] theidentified modal parameters were then used to update thefinite element (FE)model of the target structure [8 13ndash15 21]which was in turn used to develop the prediction methodsBreccolotti et al [10] established a methodology for predict-ing the vibration levels induced by railway traffic Crispino

and DrsquoApuzzo [17] measured road traffic-induced vibrationsin a heritage building in Naples and compared the results toa prediction model Ding et al [19] predicted the free fieldvibrations induced bymetro trains using the coupled periodicfinite element-boundary element (FE-BE) method Chebli etal [20] proposed a method for calculating the response ofperiodic structures induced by moving loads Some otherwork also has been done Cagnan [3] assessed the seismicperformance of an old cathedral using ambient vibration testresults Ceroni et al [4] compared the eigenfrequencies andvibrationmodes of a structuremeasured from test results andcalculated by an FE model that included the soil-structureinteraction Foti et al [6] presented the process of updatinga 3D finite element model of a building based on field testsRainieri et al [7] proposed a valuable tool for the indirectnoninvasive structural assessment of historical structuresusing the combination of ambient vibration tests and modelrefinement Cacciola and Tombari [9] made a vibratingbarrier to reduce the vibrations of structures by exploitingthe structure-soil mechanism Giulio et al [11] presentedthe main modal parameters of a church by evaluating thetest data Sevim et al [12] assessed the nonlinear seismicperformance of a restored historical masonry arch bridgeusing ambient vibrations El-Attar et al [14] proposed passivecontrol techniques to control structural vibrationsMarchisio

HindawiShock and VibrationVolume 2017 Article ID 1451483 12 pageshttpsdoiorg10115520171451483

2 Shock and Vibration

Road

A

B

Transfer path

Figure 1 Layout of the measurement points

et al [16] studied the dynamic behavior of the Leaning Towerof Pisa under different exactions

The prediction model for structural vibrations can bedivided into several parts such as the vibration sources thetransfer path of vibration waves in the free field and theinteraction between the soil and the structural foundationtherefore simulating these parts in one prediction modelis difficult In addition due to the particularities of ancientarchitecture these buildings cannot be tested too often so ifan effective vibration predictionmethod can be proposed theharm to the ancient architecture brought by the field test andlarger traffic loads will be reduced

In this paper a new prediction method in the frequencydomain is proposed and validated through a field test In thismethod the transfer ratio in the frequency domain is com-bined with an FE model to reduce the scale of the predictionmodel and the computing time Using the proposed methodthe vibration responses of the structure can be obtainedeffectively without detailed field test A field vibration testwas conducted at the Yangzhou Zhunti Temple and theupdated FE model of the sutra depository was establishedusing the identified modal parameters Then the vibrationresponses of the structure induced by larger traffic loadswere predicted using the transfer method in the frequencydomain The aim of this article is to provide an effective pre-diction method for the structural vibrations and to providea reference for researchers in the field of structural vibrationprediction under traffic loads

2 Prediction Method

The prediction model is developed as follows (1) the vibra-tions at position A near the road and at position B atthe structural foundation induced by the same vehicle aremeasured as indicated in Figure 1 (2) the transfer ratio foreach single frequency is calculated and the time history ofeach single frequency at position B is obtained (3) the modalparameters of the structure are identified by analyzing the

Measurement

FE model

Vibrationresponses of thebuilding

Modalparameters

Accelerationnear road

Upd

atin

g

Foundationacceleration

Time history ofeach singlevibration signal

Tran

sfer

func

tion

Supe

rpos

ition

Figure 2 Sketch of the prediction model

field test data (4) the FEmodel of the structure is updated andused to calculate the structural vibration responses inducedby each single vibration signal and (5) the vibrations of thebuilding can be calculated as shown in Figure 2

21 Transfer Function in the Frequency Domain If the forceacting on a multiple degrees-of-freedom (MDOF) system isdefined as a harmonic load then the dynamic equation of thesystem can be written as

MX + CX + KX = P sin 120579119905 (1)

where M C and K are the mass damping and stiffnessmatrices of the system respectively X X and X are theacceleration velocity and displacement vectors respectivelyand P is the force vector of the system

The mode is processed orthogonally

119872119899119899 + 119862119899119899 + 119870119899119884119899 = 120601119879119899P sin 120579119905 = 119875119899 sin 120579119905 (2)

where 119872119899 119862119899 and 119870119899 are the mass damping and stiffnessof the 119899th degree-of-freedom (DOF) respectively and119884 are the acceleration velocity and displacement vectorsrespectively and 119875119899 sin 120579119905 is the force of the 119899th DOF

According to structural dynamics the solution of (1) canbe expressed as

119884119899 = 120588119899 sin (120579119905 minus 120572119899) (3)

Shock and Vibration 3

where 120588119899 = (119875119899119870119899)(1radic(1 minus 120579120596119899)2 + (2120585119899120579120596119899)2) 120572119899 =tanminus1(2120585119899(120579120596119899)(1 minus 12057921205962119899)) 120596119899 = radic119870119899119872119899

X = 119873sum119894=1

120601119879119894 119884119894 = 119873sum119894=1

[120601119879119894 120588119899sin (120579119905 minus 120572119899)]= S1sin (120579119905 minus 1205721) + sdot sdot sdot + S119899sin (120579119905 minus 120572119899)=

1199031sin (120579119905 minus 1205731)1199032sin (120579119905 minus 1205732)119903119899sin (120579119905 minus 120573119899)

(4)

When 1199051 = 119905 + 2120587120579

X1015840 =

1199031sin(120579119905 + 1205792120587120579 minus 1205731)1199032sin(120579119905 + 1205792120587120579 minus 1205732)119903119899sin(120579119905 + 1205792120587120579 minus 120573119899)

= X (5)

Thus the steady-state vibration response of eachDOFhasa single frequency and the vibration frequency is the same asthe excitation frequency when an MDOF system is subjectedto a single frequency excitation

When the load in (1) changes the input loads increaselinearly with the slope 120582 then the dynamic equation of thesystem can be written as

MX + CX + KX = 120582P sin 120579119905 = Q sin 120579119905 (6)

where M C and K are the mass damping and stiffnessmatrices of the system respectively X X and X are theacceleration velocity and displacement vectors respectivelyandQ is the force vector of the system


119872119899119899 + 119862119899119899 + 119870119899119884119899 = 120601119879119899Q sin 120579119905 = 120582119875119899 sin 120579119905 (7)

The solution of (6) is

119884119899 = 120582120588119899 sin (120579119905 minus 120572119899)X = 119873sum119894=1

120601119879119894 119884119894 = 119873sum119894=1

[120601119879119894 120582120588119899 sin (120579119905 minus 120572119899)]= 120582S1 sin (120579119905 minus 1205721) + sdot sdot sdot + 120582S119899 sin (120579119905 minus 120572119899)=

1205821199031 sin (120579119905 minus 1205731)1205821199032 sin (120579119905 minus 1205732)120582119903119899 sin (120579119905 minus 120573119899)

(8)

Thus the amplitude ratio between different DOFs is con-stant when the input loads increase linearly with the slope 120582

According to classical structural dynamics the vibrationsignal at any time can be written as by a series of simpleharmonic waves

119860 (119905) = 119899sum119896=1

119860119896 (120596119896 119905 120593119896) (9)

When the vibrations and the transfer function betweentwo points are obtained the vibration of the prediction pointcan be calculated as follows

(1) Process the acceleration histories 1199091(119905) at point A and1199101(119905) at point B that are induced by the same vehicle using thefollowing Fourier transform

1198831 (120596) = int+infinminusinfin1199091 (119905) 119890minus119895120596119905119889119905

1198841 (120596) = int+infinminusinfin1199101 (119905) 119890minus119895120596119905119889119905 (10)

(2) Calculate the transfer function119867(120596) between point Aand point B

119867(120596) = 1198831 (120596)1198841 (120596) (11)

With another acceleration history 1199092(119905) the processedresult of 1199092(119905) is 1198832(120596) and the Fourier transform processedresult 1198842(120596) of the acceleration history 1199102(119905) at point B can becalculated

(3) Calculate 1199102(119905) using following function1199102 (119905) = 12120587 intinfinminusinfin 1198842 (120596) 119890119895120596119905119889120596 (12)

22 Modal Parameters Identification Structural vibrationsignals under traffic loads have the following problems (1)the input cannot be accurately known (2) the vibration sig-nals are comprehensively influenced by many vehicle loadsmaking it impossible to obtain a free attenuation signal of thestructure under a single vehicle load (3) the vibration signalsare greatly affected by environmental vibrations Based onthe above constraints the traditional methods for the modalparameters identification of structure in the time domain orin the frequency domain are not applicable for this test Yuanet al [21] proposed a new method for identifying the modalparameters by comprehensively analyzing the autocorrelationfunction frequency response function transfer function andcross-correlation function of the vibration signals

The frequency response function119867(120596) is defined as

|119867 (120596)|2 = 119866119910119910 (120596)119866119891119891 (120596) (13)

where 119866119910119910(120596) and 119866119891119891(120596) are the autopower spectra of thestructural responses and the excitation force respectively


The environmental vibration excitation is assumed to bea white noise excitation namely 119866119891119891(120596) = 119888 119888 is constantThen the natural frequencies of the structure can be obtainedusing the autopower spectra of the structural vibrationsignals The peaks corresponding to the frequency inducedby the white noise excitation are the structural naturalfrequencies However the measured structural vibrationsignals are also affected by pedestrian walking and electricalsignals often resulting in false peaks in the frequency spectraTherefore the cross-power spectral density (PSD) functionis used between different measurement points to improvethe analysis accuracy If the peaks of the auto-PSD and thecross-PSD appear at the same frequency then the frequencycorresponding to each peak can be considered one of thenatural frequencies of the structure

The frequency response function is defined as the fre-quency response ratio of the measurement point and the ref-erence point under environmental excitation The vibrationresponse at the reference point is defined as the input signaland the responses at the measurement points are the outputsignals under the influence of the environmental excitationThen the coefficients of the vibrationmodes can be defined as

Φ = 1003816100381610038161003816119867119898 (120596)10038161003816100381610038161003816100381610038161003816119867119899 (120596)1003816100381610038161003816119867 (120596) = 119878119909119910 (120596)119878119909119909 (120596)

(14)

where Φ is the coefficient of the vibration mode 119867(120596) isthe transfer function 119878119909119909(120596) is the auto-PSD function and119878119909119910(120596) is the cross-PSD functionThe sign ofΦ is determinedby the phase relationships of the cross-PSD between differentmeasurement points the sign is positive for the same phaseand it is negative for different phase [21]

23 Building Vibrations under Multisupport Excitations Thedynamic equation of a discrete building model is

M s + C s + Ks = P (15)

where M C and K are the mass damping and stiffnessmatrices of the building respectively s s and s are theacceleration velocity and displacement vectors respectivelyand P is the force vector of the building FE model

Here the large-mass method is used to excite the forcedmovement and multilumped masses are attached to theexcited positions of the building foundation The DOF alongthe 119895-direction of the excited positions is released and theforce 119875119895 is applied to the lumped-mass in the same direction

119875119895 = 1198720 1199040 (16)

where 1198720 is the virtual lumped-mass and 1199040 is the inputaccelerationThen the dynamic equation of the lumped-masscan be rewritten as

[[[[[[[[[[[[

11989811 sdot sdot sdot 1198981119895 sdot sdot sdot 1198981119899 d d1198981198951 sdot sdot sdot 1198720 sdot sdot sdot 119898119895119899 d d1198981198991 sdot sdot sdot 119898119899119895 sdot sdot sdot 119898119899119899

]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

+[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

+[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

=(((((

1199011119872119900 1199040119901119899)))))

(17)

The 119895th component of (17) is expanded as1198981198951 1199041 + sdot sdot sdot + 1198720 119904119895 + sdot sdot sdot + 119898119895119899 119904119899 + 1198881198951 1199041 + sdot sdot sdot + 119888119895119895 119904119895+ sdot sdot sdot + 119888119895119899 119904119899 + 11989611989511199041 + sdot sdot sdot + 119896119895119895119904119895 + sdot sdot sdot + 119896119895119899119904119899= 1198720 1199040(18)

The large-mass1198720 is much larger than all the remainingmass 119898 on the left side of (18) thus 119904119895 asymp 1199040 The vibrationresponses of the remaining input points of the foundation canalso be calculated using the above method

In the large-mass method the parameter of1198720 is usuallydefined as 105 times the total structure mass in this paper

3 Test of the Zhunti Temple

31 General Information The Yangzhou Zhunti Temple wasbuilt during the late Ming dynasty The distance betweenZhunti Temple and Yanfu east road is only 14m and largevehicle flows are common on this road during morning


EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500Unit (mm)

South

North

1950

Figure 3 Top view of the depository of Buddhist sutra48

5081

30 8850 96

90 1067

0 1172

0

1950 2600 1300 2600 1300 2600

Z

Y

X

Unit (mm)

Figure 4 Side view of the of Buddhist sutra depository

and evening rush hours Therefore the vibrations of sutradepository induced by the traffic loads are considerable Thesutra depository is made of wood and includes 2 floors and34 columns The columns are connected with each other byFang and beam and the connections between the beams andcolumns aremortise-tenon connectionsThe gables at easternandwestern sides of the building are constructed of brick andthe columns are located outside of the gables The top andside view of the sutra depository are shown in Figures 3 and4 respectively

The measurement points on the 1st floor and 2nd floorwere arranged near the pillars and on top of the columnsHere the top of the pillar is defined as the 3rd floor Thespecific arrangement of the measurement points is shown inFigure 5

Because the structural responses under the traffic loadsare mainly composed of low frequency signals 941B sensorswere used tomeasure the ground and the structure vibrationsdue to the micro tremors and general structural vibration

(a) On site

Z

Y

X

Measurement point

(b) Side view

X

Y

EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500

1950

Unit (mm)

North

South

1 5 9

2 6 10

4812

3711

Measurement point

(c) Top view

Figure 5 Measurement points layout

and the sensitivity of the accelerometer can meet the need ofthe required test precision According to the traffic flow inthe morning and evening the test period was divided into 3parts 630sim930 1700sim2000 and 2300sim100 The samplingfrequency of the test was 1024Hz and the sampling time ofeach group was 1200 s


minus30

minus15

0

15

30Ac

cele

ratio

n (m

ms

2)

2 4 6 8 10 12 14 16 18 200Time (min)

(a) 119883-direction

minus30

minus15

0

15

30

Acce

lera

tion

(mm

s2)

2 4 6 8 10 12 14 16 18 200Time (min)

(b) 119884-direction

Figure 6 Acceleration histories of the 2nd floor

157

64 76

408

67

1031

1X 2X 3X 1Y 2Y 3Y

Measurement points

0

2

4

6

8

10

12

Acce

lera

tion

(mm

s2)

Figure 7 The average maximum acceleration for each floor

32 Vibration in the Time Domain According to the spec-ification [23] the vibrations in the horizontal direction aretaken as the assessment value The horizontal accelerationhistories measured on the 2nd floor are shown in Figure 6

The test data acquired during morning and evening rushhours are used for statistical analysis The processing methodin the time domain is as follows (1) the test data withinone second are averaged to obtain a total of 1200 values (2)to eliminate the interference of the ambient vibration thehighest 5 of the acceleration data are deemed as invalid andexcluded the maximum value of the residual data is selectedas the representative acceleration value (3) the maximumacceleration of each measurement point in each group isobtained and (4) the average value of the representativeacceleration from the measurement points on the same flooris defined as the structural vibration response as shown inFigure 7

Thus the acceleration in 119883-direction and 119884-directionincreased at higher floors and the acceleration in119884-directionis greater than that in the 119883-direction on the same floorThe maximum acceleration in the 119883-direction and 119884-direction which occurred on the third floor was 76mms2and 1031mms2 respectively under the traffic loads duringmorning and evening rush hours

33 Vibration in the FrequencyDomain Thevibration signalsof the 2nd floor under the traffic loads during morning andevening rush hours are analyzed using spectrum analysis andthe dominant frequency bands are shown in Figure 8

Table 1 The identified first 2 natural frequencies and modal factorsof the structure

Order 1 2Direction 119883 119884Natural frequencies (Hz) 284 309Modal factors

1st floor 0 02nd floor 072 0723rd floor 1 1

The dominant frequency bands of the structural vibrationinduced by the traffic loads duringmorning and evening rushhour were 10Hzsim20Hz and the dominant frequency bandswere approximately the same in the 119883-direction and the 119884-direction for the same measurement point

The vibration signals are processed in the frequencydomain using Fourier transform However only the domi-nant frequency bands are obtained obtaining the transfer lawof each single frequency vibration signal is difficult There-fore the vibration signals are processed by one-third octaveprocessing to determine the influence of each single fre-quency vibration signal on the whole structural vibration asshown in Figure 9

The maximum vibration levels corresponding to thecentral frequencies in the 119883-direction is 593 dB on the3rd floor and the corresponding frequency is 25Hz themaximum vibration levels corresponding to the central fre-quencies in the 119884-direction is 563 dB on the 3rd floor andthe corresponding frequency is 125Hz The vibration levelscorresponding to the central frequencies in the 119883-directionand 119884-direction increased at higher floors

4 Identification of the Structural Parameters

The structural vibrations of the 2nd and 3rd floor near thesame pillar are analyzed using the autocorrelation functionand cross-correlation function as shown in Figure 10

Only the first two natural frequencies can be obtainedfrom the frequency spectra due to the interference from theambient vibration The first two natural frequencies and thenormalized modal factors are shown in Table 1

To forecast the vibration response of the structure underheavy trunks an FE model of the Buddhist sutra depository


Acce

lera

tion

(mm

s2H

z)

20 40 60 800Frequency (Hz)

0

2

4

6

8


Acce

lera

tion

(mm

s2H

z)

0

2

4

6

8

10



Figure 8 Spectrum of the vibration signals of the 2nd floor

1 2 4 8 16 32 640

20

40

60

Vibr

atio

n le

vel (

dB)

Frequency (Hz)

1st2nd3rd


1 2 4 8 16 32 640

20

40

60Vi

brat

ion

leve

l (dB

)

Frequency (Hz)

1st2nd3rd


Figure 9 One-third octave spectrum of vibration signal

was constructed The FE model of the structure is developedusing ANSYS BEAM188 elements are used to model thepillars fangs and beams of the structure and SHELL181elements are used to model the floors and roof of thestructure The elastic modulus and density of the wood are12071198904MPa and 497 kgm3 respectively The established FEmodel of the structure is shown in Figure 11

The first 2 mode shapes of the structure are shown inFigure 12

To verify the accuracy of the established FE model themodal parameters are calculated and the measured andcalculated first 2 natural frequencies of the structure are listedin Table 2 In addition Figure 13 compares the measuredand the calculated normalized coefficients of the structuralvibration modes

Table 2 The measured and calculated first 2 natural vibrationfrequencies of the structure

Order FEM (Hz) Measured (Hz) Direction1 284 284 1198832 313 309 119884

Table 2 and Figure 13 show that the relative error ofthe structural natural frequencies between the measured andcalculated values is less than 12Moreover the relative errorof the structural modal factors between the measured andcalculated is less than 178 Therefore the FE model can beused to predict the vibration response of the building underheavy trunks


0 10 20 30 40 500000

0005

0010

0015

0020

0025

Frequency (Hz)

Acce

lera

tion

(mm

s2H

z)

(a) Autopower spectrum in the119883-direction

0000

0005

0010

0015

0020

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

(b) Cross-power spectrum in the119883-direction

Acce

lera

tion

(mm

s2H

z)

0000

0005

0010

0015

0020

10 20 30 40 500Frequency (Hz)

(c) Autopower spectrum in the 119884-direction

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

0000

0002

0004

0006

0008

0010

(d) Cross-power spectrum in the 119884-direction

Figure 10 Autopower spectrum and cross-power spectrum for the 2nd and 3rd floor

5 Prediction of the Structural Vibrationunder Heavy Trunks

51 Transfer Function To obtain the vibrations near theresource the accelerometers are arranged along the side ofthe road in front of the structure and on the first floor of theBuddhist sutra depository The acceleration of the roadsideand the structural foundation induced by the same vehicle iscollected simultaneously The arrangement of measurementpoints is shown in Figure 14

The acceleration of point A and point B shown inFigure 14 induced by the same vehicle is processed Thenthe time histories of each central frequency in the one-third octave processing spectrum are obtained as shown inFigure 15 The ratio of the maximum acceleration point A tothat of point B for the same single frequency is defined as thetransfer ratio Due to the limited length of this paper onlythe acceleration time history for the frequency band 125Hzis shown in Figure 15

The acceleration induced by a typical vehicle is processedand the acceleration time histories of each central frequency

Elements Nov 13 2015222611

1

Figure 11 FE model of the depositary of Buddhist sutra

in the one-third octave processing spectrum are obtainedThe maximum acceleration values of each central frequencyare shown in Figure 16


DisplacementStep = 1Sub = 1Freq = 2835DMX = 1009

Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd

Figure 12 The first 2 vibration mode shapes of the structure

X-direction Y-direction

071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured

Figure 13 Comparison of modal factors

The single frequency vibration signals in the dominantfrequency band are the main components of the vibrationsignals therefore the vibration signals in the dominantfrequency band are analyzed in this paper The accelerationtime histories of each central frequency in the dominantfrequency band of 10Hzsim20Hz are extracted and finallythe transfer ratio of each single frequency between point Aand point B is obtained The transfer ratio for each singlefrequency between point A and point Bmay be affected by theambient vibrations and the transfer path therefore multiplegroups of test data are analyzed and the rest of the data areaveraged to eliminate some outliers The transfer ratios forfrequency 10Hz 125Hz 16Hz and 20Hz in the dominantfrequency band 10sim20Hz are shown in Table 3

Sensor

Building

A B

Road

C

Sensor Sensor

14 m


Table 3 Transfer ratios corresponding to the central frequencies

Central frequency (Hz) Transfer ratio10 06125 04516 03920 032

To verify the accuracy of the FEmodel and the rationalityof the method proposed in this paper the acceleration ofpoint A induced by a typical vehicle is analyzed In additionthe acceleration of the 2nd floor induced by the same vehiclecan be obtained using the prediction method proposed inthis paper the acceleration values at the measurement pointon the 2nd floor obtained from the field test and from theprediction method are shown in Figure 17 Additionallybecause the predicted point is close to point A and becausethe time that the vibration waves take to travel from point


0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)

(a) Acceleration history of point A

0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)

(b) Acceleration history of point B

Figure 15 Acceleration histories of points A and B at 125Hz

00

05

10

15

20

25

30

35

40

45

1 2 4 8 16 315 63Central frequency (Hz)

Point APoint CPoint B

Acce

lera

tion

(mmmiddotsminus

2)

Figure 16 The peak acceleration of the central frequency

A to the prediction point is very short the phase differencesbetween different frequency signals are neglected

Figure 17 shows that the measured acceleration is closeto the predicted accelerationTherefore the proposed predic-tion method is considered effective and accurate

52 Ground Vibration under Heavy Trunks To predict thevibration responses of the structure under heavy trunks usingthe predictionmethod the measurement points are arrangedalong a road on which the speeds and loads of the vehiclesare close to those of the vehicles on the Yanfu east road butwith a greater traffic flow and the field test is just as shown inFigure 18

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM

Figure 17 Acceleration time history at the measurement point ofthe 2nd floor

Figure 18 Field tested acceleration along a road

The measured acceleration at the roadside is consideredto be the vibration responses of point A and the vibrationresponses of point C induced by each single frequency signalare obtained using the transfer function method proposedin this paper The measured acceleration in the 119885-directionalong the side of the road is shown in Figure 19

53 Vibration Prediction The acceleration history of thefrequency band 125Hz calculated using the transfer methodis shown in Figure 20

Then the structural vibration responses induced by eachsingle frequency signal are superimposed and the super-imposed vibration response of the 2nd floor is shown inFigure 21


minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)

Figure 19 Acceleration time history at point A in the 119885-direction

minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)

Figure 20 Acceleration time histories for 125Hz

1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)

Figure 21 Acceleration time history at the prediction point on the2nd floor

Comparing Figures 19 and 21 shows that the momentwhen the peak acceleration appears at point A and at theprediction point is almost the same The correspondingpeak acceleration is 67mms2 and 93mms2 respectivelytherefore the effectiveness of this method is verified

6 Conclusion

A vibration prediction method for historical timber build-ings induced by traffic loads is proposed and validated byan in situ experiment The building FE model is updatedusing the double-confirmation analysis method based onthe auto-PSD the cross-PSD and the frequency responsefunction of the studied structure The transfer function canbe obtained by analyzing the acceleration time histories oftwo vibration points Additionally the structural vibrationresponses induced by heavy trunks are predicted using thecombination FEM and the transfer function This predictionmethod can effectively predict the vibration responses of abuilding without detailed field tests

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This study is supported by the key project of the NationalNatural Science Foundation (Grant no 51338001) and theState Fundamental Research Funds ldquo973rdquo Program (Grant no2013CB036203) of China

References

[1] S Ucak A Bayraktar T Turker and G Osmancikli ldquoFinite-element model calibration of historical masonry domes usingoperational modal testingsrdquo Journal of Performance of Con-structed Facilities vol 30 no 2 2016

[2] I Calik A Bayraktar T Turker and H Karadeniz ldquoStructuraldynamic identification of a damaged and restored masonryvault using ambient vibrationsrdquoMeasurement vol 55 pp 462ndash472 2014

[3] Z Cagnan ldquoNumerical models for the seismic assessment ofSt Nicholas Cathedral Cyprusrdquo Soil Dynamics and EarthquakeEngineering vol 39 pp 50ndash60 2012

[4] F Ceroni S Sica M Rosaria Pecce and A Garofano ldquoEvalua-tion of the natural vibration frequencies of a historical masonrybuilding accounting for SSIrdquo Soil Dynamics and EarthquakeEngineering vol 64 pp 95ndash101 2014

[5] A Bayraktar T Turker and A C Altunisik ldquoExperimentalfrequencies and damping ratios for historical masonry archbridgesrdquo Construction and Building Materials vol 75 pp 234ndash241 2015

[6] D Foti M Diaferio N I Giannoccaro and M MongellildquoAmbient vibration testing dynamic identification and modelupdating of a historic towerrdquo NDT amp E International vol 47pp 88ndash95 2012

[7] C Rainieri G Fabbrocino and G M Verderame ldquoNon-destructive characterization and dynamic identification of amodern heritage building for serviceability seismic analysesrdquoNDT and E International vol 60 pp 17ndash31 2013

[8] T Maeda Y Sugiura and T Hirai ldquoFEM modeling of thetowers in Bayon temple in Cambodia based on micro-tremormeasurementsrdquo Advances in Engineering Software vol 39 no4 pp 346ndash355 2008

[9] P Cacciola and A Tombari ldquoVibration control of structuresthrough structure-soil-structure interactionrdquo in Proceedingsof the 9th International Conference on Structural Dynamics(Eurodyn rsquo14) pp 559ndash566 Leuven Belgium September 2014

[10] M Breccolotti A L Materazzi D Salciarini C Tamagniniand F Ubertini ldquoVibrations induced by the new undergroundrailway line in Palermo Italy Experimental measurements andFEmodelingrdquo in Proceedings of the 8th International Conferenceon Structural Dynamics (EURODYN rsquo11) pp 719ndash726 July 2011

[11] G D Giulio M Vassallo G Boscato A Dal Cin and SRusso ldquoSeismic monitoring by piezoelectric accelerometers ofa damaged historical monument in downtown LrsquoAquilardquoAnnalsof Geophysics vol 57 no 6 pp 654ndash669 2014

[12] B Sevim A Bayraktar A C Altunisik S Atamturktur andF Birinci ldquoAssessment of nonlinear seismic performance ofa restored historical arch bridge using ambient vibrationsrdquoNonlinear Dynamics vol 63 no 4 pp 755ndash770 2011


[13] A Bayraktar F Birinci A C Altunisik T Turker and BSevim ldquoFinite element model updating of Senyuva historicalarch bridge using ambient vibration testsrdquoBaltic Journal of Roadand Bridge Engineering vol 4 no 4 pp 177ndash185 2009

[14] A G El-Attar A M Saleh and A H Zaghw ldquoConservationof a slender historical Mamluk-style minaret by passive controltechniquesrdquo Structural Control and Health Monitoring vol 12no 2 pp 157ndash177 2005

[15] S El-Borgi H Smaoui F Casciati K Jerbi and F KanounldquoSeismic evaluation and innovative retrofit of a historicalbuilding in Tunisiardquo Structural Control and Health Monitoringvol 12 no 2 pp 179ndash195 2005

[16] M Marchisio L Piroddi G Ranieri S V Calcina and PFarina ldquoComparison of natural and artificial forcing to studythe dynamic behaviour of bell towers in low wind context bymeans of ground-based radar interferometry the case of theLeaning Tower in Pisardquo Journal of Geophysics and Engineeringvol 11 no 5 2014

[17] M Crispino and M DrsquoApuzzo ldquoMeasurement and predictionof traffic-induced vibrations in a heritage buildingrdquo Journal ofSound and Vibration vol 246 no 2 pp 319ndash335 2001

[18] A Schiavi and L Rossi ldquoVibration perception in buildings asurvey From the historical origins to the present dayrdquo EnergyProcedia vol 78 pp 2ndash7 2015

[19] D-Y Ding S GuptaW-N Liu G Lombaert andGDegrandeldquoPrediction of vibrations induced by trains on line 8 of Beijingmetrordquo Journal of Zhejiang University SCIENCE A vol 11 no 4pp 280ndash293 2010

[20] H Chebli R Othman and D Clouteau ldquoResponse of periodicstructures due to moving loadsrdquo Comptes RendusmdashMecaniquevol 334 no 6 pp 347ndash352 2006

[21] J L Yuan H Fan and H B Chen ldquoExperimental study ofdynamic behave of Hu Qiu Pagodardquo Experimental Study ofDynamic Behave of Hu Qiu Pagoda vol 22 no 5 pp 158ndash1642005 (Chinese)

[22] M Ma V Markine W-N Liu Y Yuan and F Zhang ldquoMetrotrain-induced vibrations on historic buildings in ChengduChinardquo Journal of Zhejiang University Science A vol 12 no 10pp 782ndash793 2011

[23] GBT 50452-2008 Technical Specifications for Protection ofHistoric Buildings AgainstMan-Made Vibration China BuildingIndustry Press Beijing China 2008 (Chinese)

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Road

A

B

Transfer path


et al [16] studied the dynamic behavior of the Leaning Towerof Pisa under different exactions

The prediction model for structural vibrations can bedivided into several parts such as the vibration sources thetransfer path of vibration waves in the free field and theinteraction between the soil and the structural foundationtherefore simulating these parts in one prediction modelis difficult In addition due to the particularities of ancientarchitecture these buildings cannot be tested too often so ifan effective vibration predictionmethod can be proposed theharm to the ancient architecture brought by the field test andlarger traffic loads will be reduced

In this paper a new prediction method in the frequencydomain is proposed and validated through a field test In thismethod the transfer ratio in the frequency domain is com-bined with an FE model to reduce the scale of the predictionmodel and the computing time Using the proposed methodthe vibration responses of the structure can be obtainedeffectively without detailed field test A field vibration testwas conducted at the Yangzhou Zhunti Temple and theupdated FE model of the sutra depository was establishedusing the identified modal parameters Then the vibrationresponses of the structure induced by larger traffic loadswere predicted using the transfer method in the frequencydomain The aim of this article is to provide an effective pre-diction method for the structural vibrations and to providea reference for researchers in the field of structural vibrationprediction under traffic loads

2 Prediction Method

The prediction model is developed as follows (1) the vibra-tions at position A near the road and at position B atthe structural foundation induced by the same vehicle aremeasured as indicated in Figure 1 (2) the transfer ratio foreach single frequency is calculated and the time history ofeach single frequency at position B is obtained (3) the modalparameters of the structure are identified by analyzing the

Measurement

FE model

Vibrationresponses of thebuilding

Modalparameters

Accelerationnear road

Upd

atin

g

Foundationacceleration

Time history ofeach singlevibration signal

Tran

sfer

func

tion

Supe

rpos

ition

Figure 2 Sketch of the prediction model

field test data (4) the FEmodel of the structure is updated andused to calculate the structural vibration responses inducedby each single vibration signal and (5) the vibrations of thebuilding can be calculated as shown in Figure 2

21 Transfer Function in the Frequency Domain If the forceacting on a multiple degrees-of-freedom (MDOF) system isdefined as a harmonic load then the dynamic equation of thesystem can be written as

MX + CX + KX = P sin 120579119905 (1)

where M C and K are the mass damping and stiffnessmatrices of the system respectively X X and X are theacceleration velocity and displacement vectors respectivelyand P is the force vector of the system


119872119899119899 + 119862119899119899 + 119870119899119884119899 = 120601119879119899P sin 120579119905 = 119875119899 sin 120579119905 (2)

where 119872119899 119862119899 and 119870119899 are the mass damping and stiffnessof the 119899th degree-of-freedom (DOF) respectively and119884 are the acceleration velocity and displacement vectorsrespectively and 119875119899 sin 120579119905 is the force of the 119899th DOF

According to structural dynamics the solution of (1) canbe expressed as

119884119899 = 120588119899 sin (120579119905 minus 120572119899) (3)



X = 119873sum119894=1

120601119879119894 119884119894 = 119873sum119894=1



(4)

When 1199051 = 119905 + 2120587120579

X1015840 =


= X (5)



MX + CX + KX = 120582P sin 120579119905 = Q sin 120579119905 (6)



119872119899119899 + 119862119899119899 + 119870119899119884119899 = 120601119879119899Q sin 120579119905 = 120582119875119899 sin 120579119905 (7)


119884119899 = 120582120588119899 sin (120579119905 minus 120572119899)X = 119873sum119894=1

120601119879119894 119884119894 = 119873sum119894=1



(8)



119860 (119905) = 119899sum119896=1

119860119896 (120596119896 119905 120593119896) (9)






119867(120596) = 1198831 (120596)1198841 (120596) (11)





|119867 (120596)|2 = 119866119910119910 (120596)119866119891119891 (120596) (13)





Φ = 1003816100381610038161003816119867119898 (120596)10038161003816100381610038161003816100381610038161003816119867119899 (120596)1003816100381610038161003816119867 (120596) = 119878119909119910 (120596)119878119909119909 (120596)

(14)



M s + C s + Ks = P (15)



119875119895 = 1198720 1199040 (16)


[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

+[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

+[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

=(((((

1199011119872119900 1199040119901119899)))))

(17)







EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500Unit (mm)

South

North

1950


5081

30 8850 96

90 1067

0 1172

0

1950 2600 1300 2600 1300 2600

Z

Y

X

Unit (mm)





(a) On site

Z

Y

X

Measurement point

(b) Side view

X

Y

EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500

1950

Unit (mm)

North

South

1 5 9

2 6 10

4812

3711

Measurement point

(c) Top view




minus30

minus15

0

15

30Ac

cele

ratio

n (m

ms

2)

2 4 6 8 10 12 14 16 18 200Time (min)


minus30

minus15

0

15

30

Acce

lera

tion

(mm

s2)

2 4 6 8 10 12 14 16 18 200Time (min)



157

64 76

408

67

1031

1X 2X 3X 1Y 2Y 3Y

Measurement points

0

2

4

6

8

10

12

Acce

lera

tion

(mm

s2)

















Acce

lera

tion

(mm

s2H

z)


0

2

4

6

8


Acce

lera

tion

(mm

s2H

z)

0

2

4

6

8

10




1 2 4 8 16 32 640

20

40

60

Vibr

atio

n le

vel (

dB)

Frequency (Hz)

1st2nd3rd


1 2 4 8 16 32 640

20

40

60Vi

brat

ion

leve

l (dB

)

Frequency (Hz)

1st2nd3rd










0 10 20 30 40 500000

0005

0010

0015

0020

0025

Frequency (Hz)

Acce

lera

tion

(mm

s2H

z)


0000

0005

0010

0015

0020

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

0000

0005

0010

0015

0020

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

0000

0002

0004

0006

0008

0010








1





Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd



071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured



Sensor

Building

A B

Road

C

Sensor Sensor

14 m






0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











X = 119873sum119894=1

120601119879119894 119884119894 = 119873sum119894=1



(4)

When 1199051 = 119905 + 2120587120579

X1015840 =


= X (5)



MX + CX + KX = 120582P sin 120579119905 = Q sin 120579119905 (6)



119872119899119899 + 119862119899119899 + 119870119899119884119899 = 120601119879119899Q sin 120579119905 = 120582119875119899 sin 120579119905 (7)


119884119899 = 120582120588119899 sin (120579119905 minus 120572119899)X = 119873sum119894=1

120601119879119894 119884119894 = 119873sum119894=1



(8)



119860 (119905) = 119899sum119896=1

119860119896 (120596119896 119905 120593119896) (9)






119867(120596) = 1198831 (120596)1198841 (120596) (11)





|119867 (120596)|2 = 119866119910119910 (120596)119866119891119891 (120596) (13)





Φ = 1003816100381610038161003816119867119898 (120596)10038161003816100381610038161003816100381610038161003816119867119899 (120596)1003816100381610038161003816119867 (120596) = 119878119909119910 (120596)119878119909119909 (120596)

(14)



M s + C s + Ks = P (15)



119875119895 = 1198720 1199040 (16)


[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

+[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

+[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

=(((((

1199011119872119900 1199040119901119899)))))

(17)







EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500Unit (mm)

South

North

1950


5081

30 8850 96

90 1067

0 1172

0

1950 2600 1300 2600 1300 2600

Z

Y

X

Unit (mm)





(a) On site

Z

Y

X

Measurement point

(b) Side view

X

Y

EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500

1950

Unit (mm)

North

South

1 5 9

2 6 10

4812

3711

Measurement point

(c) Top view




minus30

minus15

0

15

30Ac

cele

ratio

n (m

ms

2)

2 4 6 8 10 12 14 16 18 200Time (min)


minus30

minus15

0

15

30

Acce

lera

tion

(mm

s2)

2 4 6 8 10 12 14 16 18 200Time (min)



157

64 76

408

67

1031

1X 2X 3X 1Y 2Y 3Y

Measurement points

0

2

4

6

8

10

12

Acce

lera

tion

(mm

s2)

















Acce

lera

tion

(mm

s2H

z)


0

2

4

6

8


Acce

lera

tion

(mm

s2H

z)

0

2

4

6

8

10




1 2 4 8 16 32 640

20

40

60

Vibr

atio

n le

vel (

dB)

Frequency (Hz)

1st2nd3rd


1 2 4 8 16 32 640

20

40

60Vi

brat

ion

leve

l (dB

)

Frequency (Hz)

1st2nd3rd










0 10 20 30 40 500000

0005

0010

0015

0020

0025

Frequency (Hz)

Acce

lera

tion

(mm

s2H

z)


0000

0005

0010

0015

0020

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

0000

0005

0010

0015

0020

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

0000

0002

0004

0006

0008

0010








1





Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd



071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured



Sensor

Building

A B

Road

C

Sensor Sensor

14 m






0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Φ = 1003816100381610038161003816119867119898 (120596)10038161003816100381610038161003816100381610038161003816119867119899 (120596)1003816100381610038161003816119867 (120596) = 119878119909119910 (120596)119878119909119909 (120596)

(14)



M s + C s + Ks = P (15)



119875119895 = 1198720 1199040 (16)


[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

+[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

+[[[[[[[[[[[[


]]]]]]]]]]]]

(((((

1199041119904119895119904119899)))))

=(((((

1199011119872119900 1199040119901119899)))))

(17)







EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500Unit (mm)

South

North

1950


5081

30 8850 96

90 1067

0 1172

0

1950 2600 1300 2600 1300 2600

Z

Y

X

Unit (mm)





(a) On site

Z

Y

X

Measurement point

(b) Side view

X

Y

EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500

1950

Unit (mm)

North

South

1 5 9

2 6 10

4812

3711

Measurement point

(c) Top view




minus30

minus15

0

15

30Ac

cele

ratio

n (m

ms

2)

2 4 6 8 10 12 14 16 18 200Time (min)


minus30

minus15

0

15

30

Acce

lera

tion

(mm

s2)

2 4 6 8 10 12 14 16 18 200Time (min)



157

64 76

408

67

1031

1X 2X 3X 1Y 2Y 3Y

Measurement points

0

2

4

6

8

10

12

Acce

lera

tion

(mm

s2)

















Acce

lera

tion

(mm

s2H

z)


0

2

4

6

8


Acce

lera

tion

(mm

s2H

z)

0

2

4

6

8

10




1 2 4 8 16 32 640

20

40

60

Vibr

atio

n le

vel (

dB)

Frequency (Hz)

1st2nd3rd


1 2 4 8 16 32 640

20

40

60Vi

brat

ion

leve

l (dB

)

Frequency (Hz)

1st2nd3rd










0 10 20 30 40 500000

0005

0010

0015

0020

0025

Frequency (Hz)

Acce

lera

tion

(mm

s2H

z)


0000

0005

0010

0015

0020

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

0000

0005

0010

0015

0020

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

0000

0002

0004

0006

0008

0010








1





Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd



071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured



Sensor

Building

A B

Road

C

Sensor Sensor

14 m






0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500Unit (mm)

South

North

1950


5081

30 8850 96

90 1067

0 1172

0

1950 2600 1300 2600 1300 2600

Z

Y

X

Unit (mm)





(a) On site

Z

Y

X

Measurement point

(b) Side view

X

Y

EastWest

2600

2600

2600

1300

1300

3500 3850 4500 3850 3500

1950

Unit (mm)

North

South

1 5 9

2 6 10

4812

3711

Measurement point

(c) Top view




minus30

minus15

0

15

30Ac

cele

ratio

n (m

ms

2)

2 4 6 8 10 12 14 16 18 200Time (min)


minus30

minus15

0

15

30

Acce

lera

tion

(mm

s2)

2 4 6 8 10 12 14 16 18 200Time (min)



157

64 76

408

67

1031

1X 2X 3X 1Y 2Y 3Y

Measurement points

0

2

4

6

8

10

12

Acce

lera

tion

(mm

s2)

















Acce

lera

tion

(mm

s2H

z)


0

2

4

6

8


Acce

lera

tion

(mm

s2H

z)

0

2

4

6

8

10




1 2 4 8 16 32 640

20

40

60

Vibr

atio

n le

vel (

dB)

Frequency (Hz)

1st2nd3rd


1 2 4 8 16 32 640

20

40

60Vi

brat

ion

leve

l (dB

)

Frequency (Hz)

1st2nd3rd










0 10 20 30 40 500000

0005

0010

0015

0020

0025

Frequency (Hz)

Acce

lera

tion

(mm

s2H

z)


0000

0005

0010

0015

0020

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

0000

0005

0010

0015

0020

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

0000

0002

0004

0006

0008

0010








1





Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd



071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured



Sensor

Building

A B

Road

C

Sensor Sensor

14 m






0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus30

minus15

0

15

30Ac

cele

ratio

n (m

ms

2)

2 4 6 8 10 12 14 16 18 200Time (min)


minus30

minus15

0

15

30

Acce

lera

tion

(mm

s2)

2 4 6 8 10 12 14 16 18 200Time (min)



157

64 76

408

67

1031

1X 2X 3X 1Y 2Y 3Y

Measurement points

0

2

4

6

8

10

12

Acce

lera

tion

(mm

s2)

















Acce

lera

tion

(mm

s2H

z)


0

2

4

6

8


Acce

lera

tion

(mm

s2H

z)

0

2

4

6

8

10




1 2 4 8 16 32 640

20

40

60

Vibr

atio

n le

vel (

dB)

Frequency (Hz)

1st2nd3rd


1 2 4 8 16 32 640

20

40

60Vi

brat

ion

leve

l (dB

)

Frequency (Hz)

1st2nd3rd










0 10 20 30 40 500000

0005

0010

0015

0020

0025

Frequency (Hz)

Acce

lera

tion

(mm

s2H

z)


0000

0005

0010

0015

0020

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

0000

0005

0010

0015

0020

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

0000

0002

0004

0006

0008

0010








1





Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd



071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured



Sensor

Building

A B

Road

C

Sensor Sensor

14 m






0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Acce

lera

tion

(mm

s2H

z)


0

2

4

6

8


Acce

lera

tion

(mm

s2H

z)

0

2

4

6

8

10




1 2 4 8 16 32 640

20

40

60

Vibr

atio

n le

vel (

dB)

Frequency (Hz)

1st2nd3rd


1 2 4 8 16 32 640

20

40

60Vi

brat

ion

leve

l (dB

)

Frequency (Hz)

1st2nd3rd










0 10 20 30 40 500000

0005

0010

0015

0020

0025

Frequency (Hz)

Acce

lera

tion

(mm

s2H

z)


0000

0005

0010

0015

0020

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

0000

0005

0010

0015

0020

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

0000

0002

0004

0006

0008

0010








1





Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd



071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured



Sensor

Building

A B

Road

C

Sensor Sensor

14 m






0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 500000

0005

0010

0015

0020

0025

Frequency (Hz)

Acce

lera

tion

(mm

s2H

z)


0000

0005

0010

0015

0020

Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

0000

0005

0010

0015

0020

10 20 30 40 500Frequency (Hz)


Acce

lera

tion

(mm

s2H

z)

10 20 30 40 500Frequency (Hz)

0000

0002

0004

0006

0008

0010








1





Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd



071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured



Sensor

Building

A B

Road

C

Sensor Sensor

14 m






0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Nov 13 2015224706

1

(a) 1st


Nov 13 2015224744

1

(b) 2nd



071

0

072

1

1

2

3

FEMMeasured

0

058

1

072

1

2

3

FEMMeasured



Sensor

Building

A B

Road

C

Sensor Sensor

14 m






0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 4minus001

000

001

Time (s)

Maximum

Acce

lera

tion

(mm

s2)


0 1 2 3 4minus0002

0000

0002

Time (s)

Maximum

Acce

lera

tion

(mm

s2)



00

05

10

15

20

25

30

35

40

45



Acce

lera

tion

(mmmiddotsminus

2)





1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(a) Measured

1 2 3 4 5 60Time (s)

minus8

minus4

0

4

8

Vert

ical

acce

lera

tion

(mm

s2)

(b) FEM







minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus100

0

100

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


minus10

0

10

Acce

lera

tion

(mm

s2)

1 2 3 4 5 6 7 8 90Time (s)


1 2 3 4 5 6 7 8 90Time (s)

minus10

0

10

Acce

lera

tion

(mm

s2)



6 Conclusion




Acknowledgments


References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

A Prediction Method of Historical Timber Buildings’ Vibrations …downloads.hindawi.com/journals/sv/2017/1451483.pdf · Vibrations Induced by Traffic Loads and Its Validation YunshiZhang,NanZhang,YanmeiCao,andHeXia