optimisationoflongitudinalseismicenergydissipation...

Research ArticleOptimisation of Longitudinal Seismic Energy DissipationSystem for Straddle-type Monorail-Cum-Road Long-SpanCable-Stayed Bridge

Xiong Liang 12 Baomu Li1 Xiaolu Liu1 and Linong Liang2

1School of Civil Engineering and Transportation South China University of Technology Guangzhou 510641 China2Guangdong Provincial Communications Planning and Design Institute Co Ltd Guangzhou 510507 China

Correspondence should be addressed to Xiong Liang lx42mailscuteducn

Received 7 March 2019 Revised 9 July 2019 Accepted 31 July 2019 Published 16 November 2019

Academic Editor Mario Terzo

Copyright copy 2019 Xiong Liang 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

To investigate the optimal longitudinal seismic energy dissipation system of straddle-type monorail-cum-road long-span cable-stayed bridges the Niutianyang Bridge was selected as the engineering background and the explicit time-domain dimension-reduced iteration method was adopted to carry out nonlinear time-history analysis To consider the dynamic characteristics oflongitudinal movable supports the static and dynamic responses of four kinds of energy dissipation systems were studiedincluding longitudinal unconstrained elastic cable viscous damper and speed lock-up devices+e damping effect of four types ofschemes in which viscous dampers were installed at piers or towers was analysed and the parameters of the viscous dampers wereoptimised +e influences of the straddle-type monorail train braking force and the running vibration of the straddle-typemonorail traffic on the parameters of the viscous dampers were analysed+is study shows that the viscous damper system had thelowest bending moment at the bottom of the tower and a smaller displacement response and the energy dissipation was the bestEach viscous damper had the highest energy dissipation efficiency when they are installed only at the main tower +e dampingeffect was better when the damping coefficient c ranged from 3500 to 5000 kNmiddot(ms)minus α and the velocity exponent α ranged from035 to 05 +e static friction of the straddle-type monorail-cum-road long-span cable-stayed bridge support can resist the trainsrsquobraking force and the parameters of the viscous damper can be selected regardless of train braking A suitably large value ofvelocity exponent αmay be required to increase the working velocity of the viscous damper to reduce the damperrsquos participation inthe process of the train crossing the bridge

1 Introduction

Straddle-type monorail-cum-road bridges fulfil the func-tions of highway and monorail traffic on a single bridgewhich can save bridge resources reduce engineering in-vestment reduce the impact of bridges on the water envi-ronment [1] and afford greater environmental protectionIn addition to these advantages the structural features ofstraddle-type monorail-cum-road long-span cable-stayedbridges such as tower height pile length and weak dampingmake their seismic response relatively unfavourable [2] andthese special bridges are generally located at key positions ofthe route +eir destruction in the earthquake can lead totraffic disruption hinder rescue work and cause huge losses

of economic and life Compared with highway cable-stayedbridges straddle-type monorail-cum-road cable-stayedbridges also shoulder the special responsibility of ensuringthe safety of trains so a mean to ensure the safety of thestructure under the action of large earthquakes and to ensurethe safety of trains is a problem that engineers have alwaysfound difficult [3]

Many scholars have studied energy dissipation systemsand the parameter optimisation problems of highway orrailway cable-stayed bridges +e control objective of cable-stayed bridges with a partially longitudinal constraint systemis to yield maximum reductions in the base forces of bridgetowers that are longitudinally restricted with the bridge deck[4] +e dynamic responses of cable-stayed bridges depend

HindawiShock and VibrationVolume 2019 Article ID 9637356 16 pageshttpsdoiorg10115520199637356

largely on the connections between towers and beams [5ndash7]During seismic excitations the tower beam consolidationsystem can reduce the longitudinal displacements of thebeam end and the top of the tower but the internal forces ofthe tower will increase significantly +e floating system iscompletely unconstrained between the tower beams andalthough the internal force responses of the towers are smallthe main girder and the top of the tower will undergo a largelongitudinal displacement A semifloating system with thevertical support between the tower and the girder is moreoften used in such projects and the structural response isreduced with the addition of suitable longitudinal restraintdevices [8ndash11] In addition few studies have examined theenergy dissipation systems of rail-cum-road cable-stayedbridges +e viscous damper system is an ideal structuralseismic system [2 12] +e damperrsquos degree of participationwhile a train is braking can be adjusted by designing thevelocity exponent of the viscous damper [3 13] A hybridcontrol scheme that includes a magnetorheological damperand a liquid viscous damper can also be used when theearthquake occurs the main beamrsquos longitudinal vibrationresponse is mainly suppressed by the liquid viscous damperand when the train brakes it is mainly suppressed by themagnetorheological damper [14] +e collapse process andfailure mechanism of rail-cum-road cable-stayed bridgeshave been studied under strong seismic excitations [15] +eeffects of uniform temperature changes on the seismic re-sponses of a cable-stayed bridge have also been discussed[16]

Some studies have examined the interaction of monorailtrains earthquakes and bridges Kim et al [17 18] studiedthe seismic responses of a monorail bridge involving thetrain-bridge interaction Lee et al [19] analysed the traffic-induced dynamic responses of a monorail steel bridge andtrain Wang et al [20] analysed the dynamic responses of amonorail bridge-vehicle coupling system on the effects ofspeed and three kinds of loads and various radii of curvatureon the dynamic responses of the monorail bridge-vehiclecoupling system However these studies focused mainly onsingle-track beam bridges not on large-span complexbridges with track beams installed

Unlike ordinary railways the maximum running speedof a straddle-type monorail train is generally less than80 kmh So the speed is low and the train grouping isgenerally nomore than six vehicles+erefore the total massis low and the trainrsquos dynamic response differs greatly fromthat of ordinary trains [21 22] +us the research results forthe energy dissipation system with monorail bridges andordinary railway cable-stayed bridges are not fully adaptedto straddle-type monorail-cum-road long-span cable-stayedbridges which require further study

To examine the longitudinal seismic energy dissipationsystem of straddle-type monorail-cum-road long-span ca-ble-stayed bridges in this study Niutianyang Bridge is usedas the actual engineering background andANSYS software isused to establish a finite element model And an explicittime-domain dimension-reduced iteration method isadopted to study the difficult key issues of longitudinalseismic energy dissipation systems such as the optimal

selection of longitudinal seismic energy dissipation systemsthe setting of the viscous damper position the optimisationof the viscous damper parameters and the effect of straddle-type monorail traffic braking and running vibration on theselection of viscous damper parameters

2 Niutianyang Bridge

Niutianyang Bridge which is the key part of the NiutianyangExpressway project in Shantou city (Figure 1) is a long-spandouble-tower three-span cable-stayed bridge currently un-der construction over the Rongjiang River in South China+e bridge span is 775 + 1661 + 468 + 1661 + 775

9552m +e auxiliary pier is designed to increase the mainspanrsquos stiffness +e main towers are diamond-shapedconcrete bridge towers A single tower is arranged with4times15 cables and the bridge adopts a semifloating system

Figure 2 shows a standard cross section of a steel trussgirder +e bridge adopts a plan of co-construction of astraddle-type monorail-cum-road the upper deck handlessix lanes of two-way automobile traffic and the lower deck isa two-line straddle-type monorail +e width and height ofthe steel truss girder are 374m and 124m respectively +estraddle-type monorail track beam adopts a continuousstructure of a steel rail beam and the standard section lengthis 151m which is arranged above the lower chord beam ofthe main bridge steel truss girder

Each main tower has three cross beams and rises to aheight of 1829m as shown in Figure 3 +e main towerfoundation adopts bored piles and 40 variable-section pilesof φ30m to φ25m are arranged under each pile capdesigned as end-bearing piles +e plane of the main towercap is a round-end dumbbell type and the plane profile ofthe entire cap is 75m (transverse)times 33m (longitudinal)

3 Analysis Theory Finite Element Model andSeismic Excitations

31 Analysis -eory To improve the efficiency of compu-tational analysis and reduce the calculation time seismicresponse analysis has been carried out with the explicit time-domain dimension-reduced iteration method proposed bySu and his coauthors the main theory can be found inreferences [23ndash25]

+e equivalent excitation vector Fj at time instant tj isassociated with the ground motion acceleration Xj and thevelocity vector _UDj of the nodes of damping at the sametime instant +e explicit expression of the structural re-sponse at each time instant can be rewritten as

Vi Ai0F0 X0_UD01113872 1113873 + Ai1F1 X1

_UD11113872 1113873 + middot middot middot + Aiiminus 1Fiminus 1

middot Ximinus 1_UDiminus 11113872 1113873 + AiiFi Xi

_UDi1113872 1113873 i 1 2 l

(1)

where the coefficient matrices Aij (j 0 1 i) can bearranged in the form as shown in Table 1 which indicatesthat only the coefficient matricesAi0 andAi1 (i 1 2 l)

in the first two columnsmust be calculated and stored whilst

2 Shock and Vibration

the other coefficient matrices in the remaining columns canbe obtained directly from those in the second column

To improve the efficiency of nonlinear iteration Vi inequation (1) can be divided into two parts with the advantageof explicit representation of the state vector +e first part is_UDi which is the only part associated with the nonlinearportion of the damping forces and the other part can bedenoted byVRi which is the remainder ofVi except for _UDiCorrespondingly equation (1) can be divided into two partsas equations (2) and (3)_UDi AD

i0F0 X0_UD01113872 1113873 + AD

i1F1 X1_UD11113872 1113873 + middot middot middot + AD

iiminus 1Fiminus 1

middot Ximinus 1_UDiminus 11113872 1113873 + AD

iiFi Xi_UDi1113872 1113873 i 1 2 l

(2)

VRi ARi0F0 X0

_UR01113872 1113873 + ARi1F1 X1

_UR11113872 1113873 + middot middot middot + ARiiminus 1Fiminus 1

middot Ximinus 1_URiminus 11113872 1113873 + AR

iiFi Xi_URi1113872 1113873 i 1 2 l

(3)

where ADij and A

Rij consist of the rows simply extracted from

Aij with respect to _UDi and VRi respectivelyIt can be observed from equation (2) that the nonlinear

iteration can now be carried out focusing only on _UDi Once

_UDi is known the other responses in VRi can be obtaineddirectly using equation (3) with no further iteration

Note that for the purpose of structural design not allstructural responses are required and only a certain numberof critical responses require focus In other words if di-mension-reduced calculation of responses can be conductedin this process the efficiency for the analysis will be furtherenhanced Obviously the explicit formulation for VRishown in equation (3) can meet this requirement Supposethat si is a critical response component of interest in VRiFrom equation (3) si can then be directly obtained as

si asi0F0 X0

_UD01113872 1113873 + asi1F1 X1

_UD11113872 1113873 + middot middot middot + asiiminus 1Fiminus 1

middot Ximinus 1_UDiminus 11113872 1113873 + as

iiFi Xi_UDi1113872 1113873 i 1 2 l

(4)

where asij is the corresponding row vector of

ARij (j 1 2 i) with respect to siIn summary with the use of the time-domain explicit

expressions of responses shown in equation (1) dimension-reduced analysis can be easily conducted in the process oftime-history analysis of the damping structure equippedwith damping devices including the dimension-reducediteration solution for the velocity components of the nodes

775

20 21 22 23 2425

Transitionpier

Auxiliary pier Transitionpier

Auxiliary pierMain tower Main tower

1661

9552

468 1661 775

182

9

Figure 1 Elevation layout of Niutianyang Bridge (unit m)

374

16 106107

124

Highway Highway

Straddle-type monorail traffic

16

Figure 2 Standard cross section of steel truss girder (unit m)

Shock and Vibration 3

of the damping devices using equation (2) and then thedimension-reduced calculation for the other critical re-sponses concerned using equation (4) +e above procedureis particularly suitable for time-history analysis of structureswith local nonlinearities and the computational cost issignificantly lower than that of the traditional nonlineartime-history analysis methods

+emethod uses the established structural finite elementmodel to perform time-history analysis under the action ofhalf-triangle and full-triangle unit pulse ground motionacceleration obtains the coefficient vector of the seismicexcitationsrsquo effect at each time point and establishes theexplicit expression of the structural dynamic response Aself-made MATLAB program is then used to complete thestructural calculation and statistical analysis of the resultsbased on the explicit expression of the dynamic response

32 Finite Element Model A finite element model of Niu-tianyang Bridge was established using the general-purposefinite element software ANSYS and five spans of the ap-proach bridge models were also established on each side toconsider their influences on the dynamic characteristics ofthe main bridge +e finite element model of NiutianyangBridge is shown in Figure 4 +e x-axis lies in the longi-tudinal direction the y-axis lies in the transverse bridgedirection and the z-axis lies in the vertical bridge direction+ree-dimensional beam elements are used to model themain girder trusses and the main towers +e shell elementsare used to simulate the highway steel bridge deck and thelower main tower which is a single-box three-room sectionand the link elements are used to simulate the stay cables+e entire model consists of 7378 elements

According to the Chinese highway bridge design spec-ification ldquoSpecifications for Design of Highway ReinforcedConcrete and Prestressed Concrete Bridges and Culvertsrdquo(JTG 3362-2018) the material parameters in the finite ele-ment model are as follows the main beam steel of the mainbridge the elastic modulus is 200times105MPa Poissonrsquos ratiois 03 the density is 7850 kgm3 and the thermal expansioncoefficient is 0000012 the cable steel the elastic modulus is205times105MPa Poissonrsquos ratio is 03 the density of the cablesteel is 7850 kgm3 and the thermal expansion coefficient is0000012 the reinforced concrete of the main tower pierand main beam of the approach bridge elastic modulus is345times104MPa Poissonrsquos ratio is 02 density is 2600 kgm3and thermal expansion coefficient is 0000010

+e effects of the pile foundation were simulated byadding spring stiffness in six directions at the bottom of thecap of the main tower +e spring stiffness was determinedby the static equivalent principle according to the conditionof the soil layer and the arrangement of the piles +e effectsof the second-stage dead load on the structurersquos dynamiccharacteristics were considered the second-stage dead loadis 286 kNm2 and is applied to the steel bridge deck and theload is converted into structural quality when the dynamiccharacteristics are calculated +e bridgersquos completion statewas obtained via the analysis in which geometric nonlineareffects including the large displacement stress-stiffeningeffects under the dead load of the bridge and the P- effectof the tower and pier were taken into consideration

+e nonlinear behavior of cables which simulated by linkelements is considered from Chinese highway bridge designspecification ldquoGuidelines for Design of Highway Cable-Stayed Bridgesrdquo (JTGT D65-01-2007 Section 624) theelastic modulus of the stay cable is modified by the Ernstformula +e formula is shown as equation (5) In the finiteelement model the nonlinear analysis of the stay cable isrealized through changing the elastic modulus of the staycable by updating the cable tension stress

E E0

1 + (cS cos α)21113872 1113873 12σ3( )1113872 1113873E0 (5)

where E is the converted elastic modulus of the stay cableconsidering the influence of the slack of cable E0 is theelastic modulus of the steel of the stay cable c is the cable

516

66

749

55

6718

29

182

9

143

523

73

38

731

169

10

9

42

75D3

33D3

D25D25

5

5 5

67

3

8 5 7

Figure 3 Elevation of main tower (unit m)

Table 1 Coefficient matrices for each time instant

Time instantCoefficient matrix

F0 F1 F2 F3 Flminus 2 Flminus 1 Flt1 A10 A11t2 A20 A21 A11t3 A30 A31 A21 A11

tlminus 2 Alminus 20 Alminus 21 Alminus 22 Alminus 23 A11tlminus 1 Alminus 10 Alminus 11 Alminus 12 Alminus 13 A21 A11tl Al0 Al1 Al2 Al3 A31 A21 A11


weight per unit volume S is the length of the stay cable α isthe angle between the stay cable and the horizontal line andσ is the cable tension stress

+e MIDAS CIVIL-FEM was also established for thecalculation of the ultimate limit state of the load capacity ofthe main bridge as shown in Figure 5 +e dynamiccharacteristics of the completion state of the NiutianyangBridge by ANSYS-FEM and MIDAS CIVIL-FEM are bothlisted in Table 2 +e main dynamic characteristics obtainedby the two different software FEM are very close indicatingthe correctness of the finite element models +e first four-order modes of the Niutianyang Bridge are shown inFigure 6

33 Seismic Excitation According to the ldquoSeismic SafetyEvaluation Report of Niutianyang Expressway EngineeringSiterdquo in the seismic response analysis the ground accelerationresponse spectrum with the exceedance probability of 4 in100 years was taken as the horizontal seismic excitation +evertical seismic excitation is two-thirds of the horizontalseismic excitation +e horizontal design acceleration re-sponse spectrum is shown in the following equation

Sa(T)

SAmax(04 + 60T) 0 sleTlt 01 s

SAmax 01 sleTltTg

SAmaxTg

T1113874 1113875

c

Tg leTlt 10 s

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

where SAmax is the maximum value of the horizontal designacceleration response spectrum of the site Tg is the char-acteristic period and c is the index and the values of thisbridge are 105 g 085 s and 10 respectively

+e ground motion acceleration time history of the sitedesign is synthesized by fitting the site design accelerationresponse spectrum and the intensity envelope functionDuring the calculation of the ground motion acceleration

time history the number of fitting control points of thetarget response spectrum is 67 the minimum period of thecontrol point is 004 s and the maximum period is 100 s+e relative error of the iterative control of the fittedspectrum and the target spectrum is controlled within 5Seven ground motion acceleration time-history sampleswith a duration of Td 65 s are shown in Figure 7 where thetime interval is 002 s and the unit of ground motion ac-celeration time history is ms2

+e explicit time-domain dimension-reduced iterationmethod described in Section 31 is used to analyse thestructural responses of the seven seismic waves +e averageof the seven seismic wave responses is taken as the finaloutput

34ComputationalAccuracyandEfficiency Nonlinear time-history analysis of the Niutianyang Bridge was conductedusing the explicit time-domain dimension-reduced iterationmethod presented in Section 31 +e structural matricesMC and K required in our method were extracted from thebaseline model of the bridge established on the ANSYSsoftware platform To demonstrate the accuracy and effi-ciency of the present approach nonlinear time-historyanalysis is also carried out using the finite element softwareANSYS In the above two methods the sample of longitu-dinal seismic excitation as shown in Figure 7(a) is taken tobe the input of ground motion

+e longitudinal displacement at midspan of the maingirder is shown in Figure 8 and the longitudinal bendingmoment at the bottom section of the main tower is shown inFigure 9 respectively It can be seen from Figures 8 and 9 thatthe results of the present method are in good agreement withthose obtained with ANSYS indicating the validity of theexplicit time-domain dimension-reduced iteration method

For computational efficiency the time required by thepresent method is 470 s whilst a total time of 26380 s isneeded when ANSYS is used for the nonlinear time-historyanalysis In fact the elapsed time of our method includes two

X

Figure 4 Finite element model of Niutianyang Bridge by software ANSYS


Figure 5 Finite element model of Niutianyang Bridge by software MIDAS CIVIL

Table 2 Niutianyang Bridge dynamic characteristics

Mode ANSYS-FEM frequency (Hz) MIDAS CIVIL-FEM frequency (Hz) Mode shape description1 0101 0101 Main beam longitudinal drift2 0216 0215 Main beam lateral bending3 0329 0328 Main beam lateral bending4 0337 0336 Main beam vertical bending5 0350 0349 Main tower longitudinal bending6 0572 0570 Main beam vertical bending7 0612 0610 Main tower lateral bending8 0629 0627 Main tower lateral bending

Nodal solutionStep = 1SUB = 1Freq = 0100778USUM (AVG)RSYS = 0DMX = 0129E ndash 03SMX = 0129E ndash 03

0

014

3E ndash

04

028

6E ndash

04

042

9E ndash

04

071

5E ndash

04

010

0E ndash

03

011

4E ndash

03

012

9E ndash

03

085

8E ndash

04

057

2E ndash

04

ZXY

MX

MN

0

027

4E ndash

04

054

8E ndash

04

082

2E ndash

04

013

7E ndash

03

019

2E ndash

03

021

9E ndash

03

024

7E ndash

03

016

4E ndash

03

011

0E ndash

03

ZXY

MN



0

033

9E ndash

04

067

7E ndash

04

010

2E ndash

03

016

9E ndash

03

023

7E ndash

03

027

1E ndash

03

030

5E ndash

03

020

3E ndash

03

013

5E ndash

03

MN ZXY

0

032

9E ndash

04

065

7E ndash

04

098

6E ndash

04

016

4E ndash

03

023

0E ndash

03

026

3E ndash

03

029

6E ndash

03

019

7E ndash

03

013

1E ndash

03

MN ZXY


Figure 6 Mode shapes of Niutianyang Bridge (a) Mode 1 (b) Mode 2 (c) Mode 3 (d) Mode 4


parts e rst part 443 s is used to calculate the coecientmatrices in the explicit expressions of the dynamic re-sponses and the second part 27 s is spent on the

dimension-reduced calculation Apparently our method hasa much lower computational cost than the traditionalnonlinear time-history analysis method

ndash4ndash3ndash2ndash1

01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(a)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(b)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(c)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(d)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(e)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(f )


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(g)

Figure 7 Samples of acceleration time history


4 Optimal Selection of Longitudinal SeismicEnergy Dissipation Systems

41 Effects of Dynamic Characteristics ofMovable Supports onSeismic Response To investigate the contribution of the dy-namic characteristics of the longitudinal spherical movablesteel supports to bridge energy dissipation for the semifloatingsystem cable-stayed bridge three case considerations of thesupportsrsquo dynamic characteristics were studied in the struc-tural seismic response analysis For case 1 the full bridge doesnot consider the dynamic characteristics of the support and

the longitudinal direction is not constrained Case 2 considersthe dynamic characteristics of the support at the main towerand auxiliary pier For case 3 the full bridge considers thedynamic characteristics of the support When the structuraldynamic analysis does not involve the dynamic stiffness of themovable support its stiffness and yield strength were con-sidered to be zero+emovable steel support was simulated bythe approximate ideal elastoplastic element Figure 10 showsthe friction slip hysteresis model Table 3 shows the dynamicparameters of the single movable support And Table 4compares the structural seismic longitudinal response results

Table 4 shows that in case 1 the full-bridge movablesupports do not consider the dynamic characteristics in case2 the main tower and auxiliary pier movable supportsconsider the dynamic stiffness and in case 3 the full-bridgemovable supports consider the dynamic stiffness the lon-gitudinal displacement of the critical sections decreases by116sim171 and 153sim224 respectively the bendingmoment at the bottom section of the main tower is reducedby 53 and 70 respectively and the bending moment ofthe auxiliary pier cap bottom is reduced by 327 and 329respectively Considering the dynamic characteristics of themovable supports the internal force and key node dis-placement were greatly reduced+erefore for the structuralseismic dynamic response analysis the dynamic charac-teristics of the longitudinal spherical movable steel supportsshould be considered to accurately reflect the structurersquosstructural dynamic characteristics and seismic dynamicresponse +e analysis results of this paper consider thedynamic characteristics of the full-bridge movable support

42 Comparison and Selection of Longitudinal Seismic EnergyDissipation Systems To optimise and select the longitudinalseismic energy dissipation system four kinds of cable-stayedbridge energy dissipation systems were studied for theconnection between the main tower and the main girder alongitudinal unconstrained system an elastic cable system aviscous damper system and a speed lock-up device system+e purpose of the comparative analysis was to determinethe influence of the four kinds of energy dissipation systemson the structural static and dynamic responses

+e unconstrained system adopts longitudinal movablesupports and considers their dynamic characteristics andother systems are superimposed on the basis of this systemDynamic parameters of the single longitudinal movablesupport are shown in Table 3 +e elastic cable system isprovided with four strands of 100ϕ7 parallel wires undereach main tower each elastic cable is 237m long and theelastic modulus is 205 times 105 MPa +e viscous dampersystem is provided with four viscous dampers under eachmain tower +e nonlinear damping force-velocity relationfor fluid viscous dampers can be analytically expressed as afractional velocity power law

f(t) sign(v)c|v|α (7)

where f(t) denotes the damping force of the viscousdamper sign(middot) denotes the sign function v denotes thenodal relative velocity between damper ends and c and α

Nonlinear time-history analysis with ANSYSExplicit time-domain dimension-reducediteration method

ndash05

ndash04

ndash03

ndash02

ndash01

0

01

02

03

04

05

Disp

lace

men

t (m

)

10 20 30 40 50 60 700Time (s)

Figure 8 Longitudinal displacement at midspan of the maingirder


times106

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

5

Bend

ing

mom

ent (

kNmiddotm

)

10 20 30 40 50 60 700Time (s)

Figure 9 Longitudinal bending moment at the bottom section ofthe main tower


denote the damping coefficient and the velocity exponent ofthe viscous damper respectively Each damperrsquos dampingcoefficient is c 3500 kNmiddot(ms)minus α and its velocity exponentα 04

+e speed lock-up device system is installed with foursets under each main tower the locking force model isexpressed by equation (7) and each speed lock-up devicersquosdamping coefficient is c 4000 kNmiddot(ms)minus α and its velocityexponent is α 2

Table 5 shows the structural response comparisons of thefour longitudinal seismic energy dissipation systems understatic action and seismic conditions

Several observations can be made from Table 5 Staticaction the viscous damper system and the speed lock-updevice system exert no constraint on the slow load of thevehicle load and temperature so the structural responseunder static action is the same as that of the unconstrainedsystem +e elastic cable system strengthens the connectionbetween the main tower and the main girder and under thevehiclersquos load the bending moment at the bottom section ofthe main tower is reduced by 213 from the unconstrained

system However under the action of temperature thebending moment at the bottom section of the main tower is852 higher than that of the unconstrained system

With seismic excitations the displacements at the endsection of the main girder of the four restraint systems aresequentially reduced Compared with the unconstrainedsystem the displacements at the end section of the maingirder of the elastic cable system the viscous damper systemand the speed lock-up device system are reduced by 386542 and 805 respectively +e displacements at the endsection of the main girder of the unconstrained system reach1033m under seismic excitations coupled with the ex-pansion and contraction caused by temperature and otheractions which will cause great difficulties in the design of thebeam expansion joint device Compared with the viscousdamper system the relative displacement of the main girderbetween the main bridge and the approach bridge of theunconstrained system the elastic cable system and the speedlock-up device system increased by 3150 503 and 26respectively whilst the bending moment at the bottomsection of the main tower increased by 386 692 and

F(δ)

K1 K1 K1

K2

K2

δ

Fy

Figure 10 Friction slip hysteresis model of the movable support

Table 3 Dynamic parameters of the movable support

Position Number of supports per pier Preyield stiffness K1 (kNm) Postyield stiffness K2 (kNm) Yield strength Fy (kN)

Transition pier 2 123750 12 2475Auxiliary pier 2 160500 16 321Main tower 2 60000 06 120

Table 4 Structural seismic longitudinal response results of the three considerations

Seismic response Case 1 Case 2 Case 3Relative displacement of the main tower and maingirder (m) 1151 0994 0942

Displacement at the top section of themain tower (m) 1403 1241 1188Displacement at the end section of the maingirder (m) 1244 1084 1033

Relative displacement of the main girder between themain bridge and the approach bridge (m) 0936 0776 0726

Bending moment at the bottom section of the maintower (MNmiddotm) 63802 60447 59331

Bending moment at the bottom section of theauxiliary pier (MNmiddotm) 10232 6882 6866


585 respectively +e viscous damper system has theminimum relative displacement of the main girder betweenthe main bridge and the approach bridge which can ef-fectively avoid the harmful collisions that may occur at theexpansion joint device under seismic excitations and it hasthe smallest bending moment at the bottom section of themain tower which can significantly reduce the scale of themain towerrsquos foundation

+e unconstrained system has the largest displacementresponse and should not be used Compared with the un-constrained system the displacement reduction of the elasticcable system is not obvious but the seismic excitations areconcentrated on the main tower which causes its bendingmoment to show a greater increase +e speed lock-updevice system can significantly reduce the displacement atthe end section of the main girder but the bending momentat the bottom section of the main tower increases greatlyand both systems require a large main tower foundation andare not suitable for adoption+e viscous damper system cansignificantly reduce the bending moment at the bottomsection of the main tower the relative displacement of themain girder between the main bridge and the approachbridge is the smallest the hysteretic energy consumption isgood and the damping effect is remarkable which is arational longitudinal seismic energy dissipation system +ebridge uses a viscous damper system

43 Comparison and Selection of Viscous Damper SettingPosition Four viscous damper setting schemes weredesigned to investigate the influence of the viscous dampersetting position on the structurersquos critical response underseismic excitations In scheme 1 four viscous dampers arearranged under each main tower In scheme 2 four viscousdampers are arranged under each main tower and two foreach auxiliary pier In scheme 3 four viscous dampers arearranged under each main tower and two for each transi-tional pier In scheme 4 four viscous dampers are arranged

under each main tower two for each auxiliary pier and twofor each transitional pier Each damperrsquos damping coefficientis c 3500kNmiddot(ms)minus α and the velocity exponent is α 04Table 6 shows the longitudinal structural response of thefour schemesrsquo viscous damper setting positions underseismic excitations

Several observations can be made from Table 6 Com-pared with scheme 1 the displacement of the top section ofthe main tower and the end section of the main girder inschemes 2 and 3 is reduced by an average of 153 and thatin scheme 4 is reduced by 251 +e relative displacementof the main girder between the main bridge and the ap-proach bridge is significantly reduced in scheme 2 throughscheme 4 reaching 655 500 and 663 respectivelyOn the basis of the viscous damper setting at the main towerthe addition of the viscous damper setting at the auxiliarypier or the transitional pier can effectively reduce the dis-placement of the structurersquos critical section

Compared with scheme 1 the bending moments at thebottom section of the main tower in scheme 2 throughscheme 4 are reduced by 28sim49 the bendingmoment ofthe auxiliary pier in schemes 2 and 4 is reduced by 231 and226 respectively and the bending moments of thetransitional piers of schemes 3 and 4 are increased by 151and 159 respectively On the basis of the viscous dampersetting at the main tower the addition of the viscous dampersetting at the auxiliary pier can reduce the critical sectionrsquosinternal force whilst the addition of the viscous dampersetting at the transitional pier is unfavourable to thefoundation of the auxiliary pier and the transitional pier

In schemes 2 to 4 the damping forces of the viscousdamper at the main tower the auxiliary pier and thetransitional pier are almost equivalent the viscous dampersettings at the auxiliary pier and the transitional pier do notreduce the tonnage of the main towerrsquos viscous damper andthe tonnage of damping force for each damper is large

Viscous dampers are expensive and difficult to maintainand its setting must consider the cost-effectiveness ratio In

Table 5 Structural response of the four longitudinal seismic energy dissipation systems

Longitudinal seismic energy dissipation system Longitudinalunconstrained system

Elastic cablesystem

Viscous dampersystem

Speed lock-updevice system

Car + train

Displacement at the end section of themain girder (m) 0109 0018 0109 0109

Bending moment at the bottom sectionof the main tower (MNmiddotm) 4194 3299 4194 4194

Temperatureaction



Seismicexcitations


Relative displacement of the maingirder between the main bridge and the

approach bridge (m)0635 0230 0153 0157


Temperature action includes a system temperature difference of 30degC a bridge deck positive temperature difference of 14degC a bridge deck negativetemperature difference of minus 7degC and a tower body temperature difference of 5degC


schemes 1 to 4 the damping cost-effectiveness ratio of theunit number damper is 067 082 082 100 in turn scheme1 has the lowest cost-effectiveness ratio and the highestdamping efficiency followed by scheme 2 and scheme 4 hasthe worst damping efficiency

+e addition of a viscous damper to the auxiliary pierand the transitional pier can reduce the critical sectiondisplacement but it is unfavourable to some critical internalforces in the auxiliary pier and the transitional pier foun-dation and increases the difficulty and cost of maintenanceAs far as the bridge is concerned the damping effect ofscheme 1 has already met the design requirements and inconsideration of the full life-cycle cost and cost-effectivenessratio the bridge adopts scheme 1 in which viscous dampersare positioned only at the main tower

5 Parameter Optimisation of Viscous Damper

51 Selection of Viscous Damper Parameters To reasonablydetermine the value of the viscous damper parameters for theseismic excitations with an exceedance probability of 4 in100 years under different combinations of viscous damperparameters an explicit time-domain dimension-reduced it-eration method is carried out for nonlinear time-historyanalysis of the bridge +e law between the viscous damperparameters and the structurersquos seismic response are studiedFour viscous dampers are installed between the lower cross-beam of the main tower and the bottom plate of the maingirder for each main tower and a total of eight viscousdampers are installed in the whole bridge as illustrated inFigure 11 Under the same working conditions a uniformdamper damping coefficient cand velocity exponent α aretaken+e damping coefficient c of the viscous damper rangesfrom 1000 to 6000 kNmiddot(ms)minus α in increments of500 kNmiddot(ms)minus α+e velocity exponent α varies from 02 to 07in increments of 01+e number of analytical conditions is 66

+e relationship between the viscous damper parametersand the longitudinal displacement of the end section of themain girder under seismic excitation is shown in Figure 12

+e relationship between the viscous damper parametersand the longitudinal displacement of the top section of themain tower is shown in Figure 13 +e relationship betweenthe viscous damper parameters and the longitudinal bendingmoment at the bottom section of the main tower is shown inFigure 14 +e relationship between the viscous damperparameters and the viscous damper seismic stroke is shownin Figure 15

Several observations can be made from Figures 12 and13 Under the same damping coefficient c the longitudinaltop section of themain tower and the end section of themaingirder increase slowly as the velocity exponent α increasesUnder the same velocity exponent α the longitudinal topsection of the main tower and the end section of the maingirder decrease as the damping coefficient c increases theeffect changes greatly the attenuation is fast and the lon-gitudinal displacement is sensitive to the damping coefficientc When the damping coefficient c is greater than5000 kNmiddot(ms)minus α the magnitude of the longitudinal dis-placement of the girder end and the main tower top de-creases with a limited increase in the damping coefficient

Several other observations can be made from Figure 14When the damping coefficient c is less than5000 kNmiddot(ms)minus α the longitudinal bending moment at thebottom section of the main tower increases slowly as thevelocity exponent α increases However when the dampingcoefficient c is 5000 kNmiddot(ms)minus α or greater the longitudinalbending moment at the bottom section of the main towerdecreases slowly as the velocity exponent α increases andthen increases slowly When the velocity exponent α is lessthan 035 the longitudinal bending moment at the bottomsection of the main tower decreases as the damping co-efficient c increases and then increases slowly howeverwhen the velocity exponent α is 035 or greater the longi-tudinal bending moment at the bottom section of the maintower decreases as the damping coefficient increases Whenthe damping coefficient c is between 1000 kNmiddot(ms)minus α and3500 kNmiddot(ms)minus α the bending moment effect decays morerapidly

Table 6 Longitudinal structural response of the four schemes viscous damper setting positions

Viscous damper setting position Scheme 1 Scheme 2 Scheme 3 Scheme 4Displacement of the top section of the maintower (m) 0617 0531 0513 0460

Displacement of the end section of the maingirder (m) 0473 0399 0403 0355

Relative displacement of the main girder between themain bridge and the approach bridge (m) 0153 0053 0077 0052

Bending moment at the bottom section of the maintower (MNmiddotm) 43791 42547 42229 41651

Bending moment at the bottom section of theauxiliary pier (MNmiddotm) 6649 5110 6689 5148

Bending moment at the bottom section of thetransitional pier (MNmiddotm) 5862 5893 6773 6792

Damping force of the damper at the main tower (kN) 34334 33857 33915 33756Damping force of the damper at the auxiliarypier (kN) mdash 33290 mdash 33048

Damping force of the damper at the transitionalpier (kN) mdash mdash 31169 30008


Figure 15 shows that the viscous damper stroke de-creases as the damping coefficient c increases and increasesslowly as the velocity exponent α increases When thedamping coefficient c is greater than 5000 the damper strokereduction slows

To reasonably control the basic scale of the main towerand reduce the size of the expansion joint and the viscousdamper the seismic isolation design prioritises the propercontrol of the structurersquos internal force response and sec-ondly controls the structurersquos critical displacement responseas much as possible and must also consider the full life-cycle

Columns of main tower

Lower cross beam of main tower

Viscous damper

Main girder

Viscous damper


(a)


Main girder

Viscous damperViscous damper


(b)

Figure 11 Locations of viscous dampers between the main tower and main girder (a) Planar graph (b) Elevation graph

04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000

Damping coefficient (kN(ms))α

Velocity index α

Disp

lace

men

t (m

)

5000 6000

Figure 12 Longitudinal displacement of the end section of themain girder

04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000

Figure 13 Longitudinal displacement of the top section of themain tower

40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000

Figure 15 Viscous damper seismic stroke


cost of the viscous damper Comprehensive consideration ofSection 43 and this section shows that the reasonable rangesfor the bridgersquos viscous damper parameters are a dampingcoecient c 3500sim5000 kNmiddot(ms)minus α and a velocity expo-nent α 035sim05

52 Inuence of Straddle-typeMonorail Trac Braking on theSelection of Viscous Damper Parameters With reference tothe normal railway train braking-force loading time course[13] the braking force-loading time-history curve of thestraddle-type monorail train at an initial speed of 80 kmh isshown in Figure 16 where w is the trainrsquos self-weight thetrain deceleration varies from 00 to 01 g for a duration of6 s the maximum deceleration time is 1881 s and thebraking deceleration peak value is 020 g Considering acombination of four damper parameters the damping co-ecient is c 1000 kNmiddot(ms)minus α or c 6000 kNmiddot(ms)minus α andthe velocity exponent is α 02 or α 07 e two-linestraddle-monorail train has the same direction and the sameposition braking action and stops in the main span which isthe most unfavourable situation for the bridge

e longitudinal deformation of the movable support atthe main tower is shown in Figure 17 And the frictionalforce of the movable support at the main tower is shown inFigure 18 and the longitudinal bending moment at thebottom section of the main tower is shown in Figure 19

Several observations can be made from Figures 17 to 19During the straddle-type monorail trainrsquos braking processthe deformation of the movable support at the main towergradually increases e bridge is freely attenuated after thetrain brake stops on the bridge e peak friction of themovable support at the main tower decreases slowly as thedamping coecient c increases and increases as the velocityexponent α increases In the four-damper parameter com-bination the peak value of the friction of the movablesupport is 1021 kN as shown in Figure 18 which is smallerthan the yielding force Fy 120 kN in Table 2 and there isno relative sliding of the movable support e deformationof the movable support is the internal deformation of thestructural material Relative sliding of the support does notoccur which can also be explained from the static analysise straddle-type monorail trac adopts a two-line designthe train load design axle weight is 140 kN and is grouped bysix vehicles with a total weight of 6720 kN When the peakvalue of the deceleration of the twin-line train is 020 g thecorresponding maximum total braking force is 1344 kNwhich is less than the yielding force of 2754 kN provided byall supports of the main bridge in Table 3 and relativeslipping of the movable support will not occur

e peak value of the longitudinal bending moment ofthe bottom section of the main tower slowly increases as thedamping coecient c increases and decreases as the velocityexponent α increases e maximum value of the longitu-dinal bending moment of the bottom section of the maintower is 22410 kNmiddotm as shown in Figure 19 which is muchsmaller than the peak of the seismic excitations estraddle-type monorail trac braking eect does not controlthe structural design

Due to the small total mass of the straddle monorail andthe low initial braking velocity the static friction of thestraddle-type monorail-cum-road long-span cable-stayedbridge support can resist the trainrsquos braking force Duringthe trainrsquos braking process no viscous damper is required toparticipate in the work and the parameters of the viscousdamper can be selected regardless of the train braking

53 Inuence of Straddle-type Monorail Trac Running onthe Selection of Viscous Damper Parameters Regardless ofrunning comfort and other issues the moving load is used tosimulate the running process of the straddle-type monorailtrac and the relationship between the bridgersquos longitudinalresponse and the viscous damper parameters is studiedConsider a four-damper parameter combination thedamping coecient is c 1000 kNmiddot(ms)minus α or

Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g

Figure 16 Braking force-loading time-history curve

c = 1000kN(ms)02 α = 02c = 1000kN(ms)07 α = 07c = 6000kN(ms)02 α = 02c = 6000kN(ms)07 α = 07

0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521

Figure 17 Longitudinal deformation of the movable support


c 6000 kNmiddot(ms)minus α and the velocity exponent is α 02 orα 07 +e train consists of one first vehicle + four standardvehicles + one first vehicle the standard vehicle length is148m and the first vehicle length is 155m In the analysiseach vehiclersquos axle load is represented by four concentratedforces (4 times 140 kN) +e vehiclersquos axle load is simplified intoa series of moving concentrated forces the action position isthe actual action point of each wheel and the concentrationforce is equal to the wheel axle load +e straddle-type

monorail traffic running speed is v 80 kmh +e simpli-fied loading model of a straddle-type monorail traffic run-ning cable-stayed bridge is shown in Figure 20 Eachconcentrated force is numbered as pi according to the di-rection in which the train travels Assuming that the two-linestraddle-monorail traffic has the same direction and thesame speed running across the cable-stayed bridge the firstconcentrated force enters the bridge at the initial zero timethe time of the i-th load entering the bridge can be expressedas ti liv

+e longitudinal displacement of the end section of themain girder is shown in Figure 21 and the viscous damperdamping force is shown in Figure 22

It can be seen from Figures 21 and 22 that the maximumdamper peak value is 38mm and the maximum dampingforce peak value is 3617 kN +e peak value of the structuralresponse is small while the train is running much smallerthan the peak value of seismic excitations and the structuraldesign is not controlled by the running process of thestraddle-type monorail traffic +e viscous damper is notrequired to suppress the structurersquos longitudinal vibrationwhile the straddle-type monorail traffic is running

+e viscous damper is set for an earthquake with a lowprobability of occurrence During the trainrsquos daily runningthe longitudinal velocity of the main girder is much lowerthan that during a strong earthquake +e seismic viscousdamper is also working which makes the viscous dampereasy to wear the viscous damper design is not required toaccount for the low-speed conditions of the trainrsquos dailyrunning Because the longitudinal vibration velocity of themain girder is low (14mms) while the train is running andthe damping force decreases rapidly as the velocity exponentα increases the damping force is sensitive to the velocityexponent α +erefore the velocity exponent α can take asuitably large value to increase the viscous damperrsquos workingvelocity to reduce the damperrsquos participation in the processof the train crossing the bridge thereby improving thedurability of the viscous damper However when the ve-locity exponent α is large the seismic efficiency of theviscous damper will be affected After comprehensiveconsideration of the earthquakersquos action the trainsrsquo runningaction and the life-time cost of viscous dampers the bridgeviscous damper is designed with a damping coefficientc 4000 kNmiddot(ms)minus α and a velocity exponent α 04

6 Conclusions

A longitudinal seismic energy dissipation system forstraddle-type monorail-cum-road long-span cable-stayedbridge has been selected and optimised in this study

(1) Compared with the unconstrained system the elasticcable system and the speed lock-up device theviscous damper system can significantly reduce thebending moment at the bottom section of the maintower +e relative displacement of the main girderbetween the main bridge and the approach bridge isthe lowest the hysteretic energy consumption isgood and the damping effect is remarkable thus it is


0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021

Figure 18 Frictional force of the movable support

0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04




an ideal longitudinal seismic energy dissipationsystem for straddle-type monorail-cum-road long-span cable-stayed bridges

(2) +e damping efficiency of the unit number damper isthe highest with the viscous damper installed only atthe main tower and the damper effect is the bestwhen the viscous damper is installed both at themain tower and at the auxiliary pier but the tran-sitional pier is unfavourable when the viscousdamper is installed at the transitional pier

(3) In general the critical response of a straddle-typemonorail-cum-road long-span cable-stayed bridgedecreases as the damping coefficient increases andincreases slowly as the velocity exponent increasesbut the longitudinal bending moment at the bottomsection of the main tower does not change mono-tonically with the damper parameters

(4) Due to the small total mass of the straddle monorailand the low initial braking velocity the static friction

of the straddle-type monorail-cum-road long-spancable-stayed bridge support can resist the trainrsquosbraking force and the parameters of the viscousdamper can be selected regardless of train braking

(5) While straddle-type monorail traffic is running theviscous damper is not required to suppress thestructurersquos longitudinal vibration and it can take asuitably large value of velocity exponent α to increasethe working velocity of the viscous damper to reducethe damperrsquos participation in the process of the traincrossing the bridge thereby improving the durabilityof the viscous damper

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3

pi = 140kN v = 80kmh

Figure 20 Simplified loading model of a straddle-type monorail traffic running cable-stayed bridge

0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617

Figure 22 Viscous damper damping force


Acknowledgments

+is work was supported by the National Natural ScienceFoundation of China (51678252) and the Science andTechnology Program of Guangzhou China (201804020069)

References

[1] Z Y Gao ldquoTechnical characteristics of main bridge of HutongChangjiang river bridgerdquo Bridge Construction vol 44 no 2pp 1ndash5 2014 in Chinese

[2] H S Ruan A P Qu Y D He and L A Li ldquoStudy ofstructural seismic response characteristics of long span rail-cum-road steel truss girder cable-stayed bridgesrdquo BridgeConstruction vol 45 no 2 pp 32ndash38 2015 in Chinese

[3] H S Ruan L A Li G W Yang and Y D He ldquoStudy ofseismic techniques for Huanggang Changjiang river rail-cum-road bridgerdquo Bridge Construction vol 43 no 6 pp 34ndash392013 in Chinese

[4] F F Geng and Y L Ding ldquoMultiobjective optimal control oflongitudinal seismic response of a multitower cable-stayedbridgerdquo Shock and Vibration vol 2016 Article ID 6217587p 13 2016

[5] C He S Z Qiang and M Liu ldquoAnalysis of different lon-gitudinal restraint conditions in main girder and their effectson the seismic behaviour of Wuhan white shoal Yangtz riverbridgerdquo China Journal of Highway and Transport vol 12no 4 pp 22ndash28 1999 in Chinese

[6] D Wang and P M Huang ldquoResearch on deck-tower con-nection of super long-span cable-stayed bridgerdquo Journal ofZhengzhou University (Engineering Science) vol 29 no 4pp 112ndash115 2008 in Chinese

[7] Z G Guan H You and J Z Li ldquoLateral isolation system of along-span cable-stayed bridge with heavyweight concretegirder in a high seismic regionrdquo Journal of Bridge Engineeringvol 22 no 1 Article ID 04016104 2017

[8] B B Soneji and R S Jangid ldquoPassive hybrid systems forearthquake protection of cable-stayed bridgerdquo EngineeringStructures vol 29 no 1 pp 57ndash70 2007

[9] A J Ye S D Hu and L C Fan ldquoSeismic displacementcontrol for super-long-span cable-stayed bridgesrdquo China CivilEngineering Journal vol 37 no 12 pp 38ndash43 2004 inChinese

[10] S P Wu C Zhang and Z Z Fang ldquoDesign schemes andparameter regression analysis of viscous dampers for cable-stayed bridgerdquo Bridge Construction vol 44 no 5 pp 21ndash262014 in Chinese

[11] C Y Jiao J Z Li and T B Peng ldquoEffects of differentconnecting styles between towers and deck on seismic re-sponses of a long-span cable-stayed bridgerdquo Journal of Vi-bration and Shock vol 28 no 10 pp 179ndash234 2009 inChinese

[12] H Guo Y Q Li S T Hu and X L Ban ldquoResearch onearthquake response of highway and railway shared cable-stayed bridge with 532m-main span and vibration-reducingeffect of damperrdquo Railway Engineering vol 1 pp 14ndash18 2015in Chinese

[13] L Lyu and J Z Li ldquoStudy on vibration control effect of viscousdampers for rail-cum-road cable-stayed bridge duringearthquake train braking and runningrdquo Engineering Me-chanics vol 32 no 12 pp 139ndash146 2015 in Chinese

[14] S Q Qin and W L Qu ldquoHybrid control of longitudinalvibration responses in deck of Tianxingzhou rail-cum-roadcable-stayed bridge caused by earthquake train braking and

vehicle moving loadsrdquo Bridge Construction vol 4 pp 1ndash92008 in Chinese

[15] X W Wang B Zhu and S G Cui ldquoResearch on collapseprocess of cable-stayed bridges under strong seismic excita-tionsrdquo Shock and Vibration vol 2017 Article ID 718528118 pages 2017

[16] J Guo J Zhong X Dang andW Yuan ldquoSeismic responses ofa cable-stayed bridge with consideration of uniform tem-perature loadrdquo Applied Sciences vol 6 no 12 p 408 2016

[17] C-W Kim M Kawatani C-H Lee and N NishimuraldquoSeismic response of a monorail bridge incorporating train-bridge interactionrdquo Structural Engineering and Mechanicsvol 26 no 2 pp 111ndash126 2007

[18] C-W Kim and M Kawatani ldquoEffect of train dynamics onseismic response of steel monorail bridges under moderateground motionrdquo Earthquake Engineering amp Structural Dy-namics vol 35 no 10 pp 1225ndash1245 2006

[19] C H Lee M Kawatani C W Kim N Nishimura andY Kobayashi ldquoDynamic response of a monorail steel bridgeunder a moving trainrdquo Journal of Sound and Vibrationvol 294 no 3 pp 562ndash579 2006

[20] HWang E Zhu and Z Chen ldquoDynamic response analysis ofthe straddle-type monorail bridge-vehicle coupling systemrdquoUrban Rail Transit vol 3 no 3 pp 172ndash181 2017

[21] R Wei and J Li ldquoSummary of research on vehicle-bridgevibration of straddle-type monorail transportationrdquo AutoIndustry Research vol 9 pp 44ndash49 2018 in Chinese

[22] Y L Li Q F Qiao K J Chen Y P Zeng and H Y XiangldquoStudy of vehicle-induced longitudinal vibration and con-nection between pylon and girder of long span railway cable-stayed bridgerdquo Bridge Construction vol 44 no 2 pp 12ndash192014 in Chinese

[23] C Su B M Li T C Chen X Liang and X H DaildquoNonlinear random vibration analysis of energy-dissipationstructures with viscous dampers by random simulationmethod based on explicit time-domain dimension-reducediteration schemerdquo Chinese Journal of Computational Me-chanics vol 33 no 4 pp 556ndash563 2016 in Chinese

[24] C Su X Liu B Li and Z Huang ldquoInelastic response analysisof bridges subjected to non-stationary seismic excitations byefficient MCS based on explicit time-domain methodrdquoNonlinear Dynamics vol 94 no 3 pp 2097ndash2114 2018

[25] C Su B Li T Chen and X Dai ldquoStochastic optimal design ofnonlinear viscous dampers for large-scale structures subjectedto non-stationary seismic excitations based on dimension-reduced explicit methodrdquo Engineering Structures vol 175pp 217ndash230 2018


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

largely on the connections between towers and beams [5ndash7]During seismic excitations the tower beam consolidationsystem can reduce the longitudinal displacements of thebeam end and the top of the tower but the internal forces ofthe tower will increase significantly +e floating system iscompletely unconstrained between the tower beams andalthough the internal force responses of the towers are smallthe main girder and the top of the tower will undergo a largelongitudinal displacement A semifloating system with thevertical support between the tower and the girder is moreoften used in such projects and the structural response isreduced with the addition of suitable longitudinal restraintdevices [8ndash11] In addition few studies have examined theenergy dissipation systems of rail-cum-road cable-stayedbridges +e viscous damper system is an ideal structuralseismic system [2 12] +e damperrsquos degree of participationwhile a train is braking can be adjusted by designing thevelocity exponent of the viscous damper [3 13] A hybridcontrol scheme that includes a magnetorheological damperand a liquid viscous damper can also be used when theearthquake occurs the main beamrsquos longitudinal vibrationresponse is mainly suppressed by the liquid viscous damperand when the train brakes it is mainly suppressed by themagnetorheological damper [14] +e collapse process andfailure mechanism of rail-cum-road cable-stayed bridgeshave been studied under strong seismic excitations [15] +eeffects of uniform temperature changes on the seismic re-sponses of a cable-stayed bridge have also been discussed[16]

Some studies have examined the interaction of monorailtrains earthquakes and bridges Kim et al [17 18] studiedthe seismic responses of a monorail bridge involving thetrain-bridge interaction Lee et al [19] analysed the traffic-induced dynamic responses of a monorail steel bridge andtrain Wang et al [20] analysed the dynamic responses of amonorail bridge-vehicle coupling system on the effects ofspeed and three kinds of loads and various radii of curvatureon the dynamic responses of the monorail bridge-vehiclecoupling system However these studies focused mainly onsingle-track beam bridges not on large-span complexbridges with track beams installed

Unlike ordinary railways the maximum running speedof a straddle-type monorail train is generally less than80 kmh So the speed is low and the train grouping isgenerally nomore than six vehicles+erefore the total massis low and the trainrsquos dynamic response differs greatly fromthat of ordinary trains [21 22] +us the research results forthe energy dissipation system with monorail bridges andordinary railway cable-stayed bridges are not fully adaptedto straddle-type monorail-cum-road long-span cable-stayedbridges which require further study

To examine the longitudinal seismic energy dissipationsystem of straddle-type monorail-cum-road long-span ca-ble-stayed bridges in this study Niutianyang Bridge is usedas the actual engineering background andANSYS software isused to establish a finite element model And an explicittime-domain dimension-reduced iteration method isadopted to study the difficult key issues of longitudinalseismic energy dissipation systems such as the optimal

selection of longitudinal seismic energy dissipation systemsthe setting of the viscous damper position the optimisationof the viscous damper parameters and the effect of straddle-type monorail traffic braking and running vibration on theselection of viscous damper parameters

2 Niutianyang Bridge

Niutianyang Bridge which is the key part of the NiutianyangExpressway project in Shantou city (Figure 1) is a long-spandouble-tower three-span cable-stayed bridge currently un-der construction over the Rongjiang River in South China+e bridge span is 775 + 1661 + 468 + 1661 + 775

9552m +e auxiliary pier is designed to increase the mainspanrsquos stiffness +e main towers are diamond-shapedconcrete bridge towers A single tower is arranged with4times15 cables and the bridge adopts a semifloating system

Figure 2 shows a standard cross section of a steel trussgirder +e bridge adopts a plan of co-construction of astraddle-type monorail-cum-road the upper deck handlessix lanes of two-way automobile traffic and the lower deck isa two-line straddle-type monorail +e width and height ofthe steel truss girder are 374m and 124m respectively +estraddle-type monorail track beam adopts a continuousstructure of a steel rail beam and the standard section lengthis 151m which is arranged above the lower chord beam ofthe main bridge steel truss girder

Each main tower has three cross beams and rises to aheight of 1829m as shown in Figure 3 +e main towerfoundation adopts bored piles and 40 variable-section pilesof φ30m to φ25m are arranged under each pile capdesigned as end-bearing piles +e plane of the main towercap is a round-end dumbbell type and the plane profile ofthe entire cap is 75m (transverse)times 33m (longitudinal)

3 Analysis Theory Finite Element Model andSeismic Excitations

31 Analysis -eory To improve the efficiency of compu-tational analysis and reduce the calculation time seismicresponse analysis has been carried out with the explicit time-domain dimension-reduced iteration method proposed bySu and his coauthors the main theory can be found inreferences [23ndash25]

+e equivalent excitation vector Fj at time instant tj isassociated with the ground motion acceleration Xj and thevelocity vector _UDj of the nodes of damping at the sametime instant +e explicit expression of the structural re-sponse at each time instant can be rewritten as

Vi Ai0F0 X0_UD01113872 1113873 + Ai1F1 X1

_UD11113872 1113873 + middot middot middot + Aiiminus 1Fiminus 1

middot Ximinus 1_UDiminus 11113872 1113873 + AiiFi Xi

_UDi1113872 1113873 i 1 2 l

(1)

where the coefficient matrices Aij (j 0 1 i) can bearranged in the form as shown in Table 1 which indicatesthat only the coefficient matricesAi0 andAi1 (i 1 2 l)

in the first two columnsmust be calculated and stored whilst




i0F0 X0_UD01113872 1113873 + AD


iiminus 1Fiminus 1


iiFi Xi_UDi1113872 1113873 i 1 2 l

(2)

VRi ARi0F0 X0

_UR01113872 1113873 + ARi1F1 X1



iiFi Xi_URi1113872 1113873 i 1 2 l

(3)

where ADij and A






si asi0F0 X0

_UD01113872 1113873 + asi1F1 X1



iiFi Xi_UDi1113872 1113873 i 1 2 l

(4)




775

20 21 22 23 2425

Transitionpier



1661

9552

468 1661 775

182

9


374

16 106107

124

Highway Highway


16









E E0

1 + (cS cos α)21113872 1113873 12σ3( )1113872 1113873E0 (5)


516

66

749

55

6718

29

182

9

143

523

73

38

731

169

10

9

42

75D3

33D3

D25D25

5

5 5

67

3

8 5 7










Sa(T)


SAmax 01 sleTltTg

SAmaxTg

T1113874 1113875

c

Tg leTlt 10 s

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)








X







0

014

3E ndash

04

028

6E ndash

04

042

9E ndash

04

071

5E ndash

04

010

0E ndash

03

011

4E ndash

03

012

9E ndash

03

085

8E ndash

04

057

2E ndash

04

ZXY

MX

MN

0

027

4E ndash

04

054

8E ndash

04

082

2E ndash

04

013

7E ndash

03

019

2E ndash

03

021

9E ndash

03

024

7E ndash

03

016

4E ndash

03

011

0E ndash

03

ZXY

MN



0

033

9E ndash

04

067

7E ndash

04

010

2E ndash

03

016

9E ndash

03

023

7E ndash

03

027

1E ndash

03

030

5E ndash

03

020

3E ndash

03

013

5E ndash

03

MN ZXY

0

032

9E ndash

04

065

7E ndash

04

098

6E ndash

04

016

4E ndash

03

023

0E ndash

03

026

3E ndash

03

029

6E ndash

03

019

7E ndash

03

013

1E ndash

03

MN ZXY







01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(a)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(b)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(c)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(d)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(e)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(f )


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(g)












ndash05

ndash04

ndash03

ndash02

ndash01

0

01

02

03

04

05

Disp

lace

men

t (m

)

10 20 30 40 50 60 700Time (s)



times106

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

5

Bend

ing

mom

ent (

kNmiddotm

)

10 20 30 40 50 60 700Time (s)









F(δ)

K1 K1 K1

K2

K2

δ

Fy






















Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




i0F0 X0_UD01113872 1113873 + AD


iiminus 1Fiminus 1


iiFi Xi_UDi1113872 1113873 i 1 2 l

(2)

VRi ARi0F0 X0

_UR01113872 1113873 + ARi1F1 X1



iiFi Xi_URi1113872 1113873 i 1 2 l

(3)

where ADij and A






si asi0F0 X0

_UD01113872 1113873 + asi1F1 X1



iiFi Xi_UDi1113872 1113873 i 1 2 l

(4)




775

20 21 22 23 2425

Transitionpier



1661

9552

468 1661 775

182

9


374

16 106107

124

Highway Highway


16









E E0

1 + (cS cos α)21113872 1113873 12σ3( )1113872 1113873E0 (5)


516

66

749

55

6718

29

182

9

143

523

73

38

731

169

10

9

42

75D3

33D3

D25D25

5

5 5

67

3

8 5 7










Sa(T)


SAmax 01 sleTltTg

SAmaxTg

T1113874 1113875

c

Tg leTlt 10 s

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)








X







0

014

3E ndash

04

028

6E ndash

04

042

9E ndash

04

071

5E ndash

04

010

0E ndash

03

011

4E ndash

03

012

9E ndash

03

085

8E ndash

04

057

2E ndash

04

ZXY

MX

MN

0

027

4E ndash

04

054

8E ndash

04

082

2E ndash

04

013

7E ndash

03

019

2E ndash

03

021

9E ndash

03

024

7E ndash

03

016

4E ndash

03

011

0E ndash

03

ZXY

MN



0

033

9E ndash

04

067

7E ndash

04

010

2E ndash

03

016

9E ndash

03

023

7E ndash

03

027

1E ndash

03

030

5E ndash

03

020

3E ndash

03

013

5E ndash

03

MN ZXY

0

032

9E ndash

04

065

7E ndash

04

098

6E ndash

04

016

4E ndash

03

023

0E ndash

03

026

3E ndash

03

029

6E ndash

03

019

7E ndash

03

013

1E ndash

03

MN ZXY







01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(a)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(b)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(c)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(d)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(e)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(f )


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(g)












ndash05

ndash04

ndash03

ndash02

ndash01

0

01

02

03

04

05

Disp

lace

men

t (m

)

10 20 30 40 50 60 700Time (s)



times106

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

5

Bend

ing

mom

ent (

kNmiddotm

)

10 20 30 40 50 60 700Time (s)









F(δ)

K1 K1 K1

K2

K2

δ

Fy






















Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








E E0

1 + (cS cos α)21113872 1113873 12σ3( )1113872 1113873E0 (5)


516

66

749

55

6718

29

182

9

143

523

73

38

731

169

10

9

42

75D3

33D3

D25D25

5

5 5

67

3

8 5 7










Sa(T)


SAmax 01 sleTltTg

SAmaxTg

T1113874 1113875

c

Tg leTlt 10 s

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)








X







0

014

3E ndash

04

028

6E ndash

04

042

9E ndash

04

071

5E ndash

04

010

0E ndash

03

011

4E ndash

03

012

9E ndash

03

085

8E ndash

04

057

2E ndash

04

ZXY

MX

MN

0

027

4E ndash

04

054

8E ndash

04

082

2E ndash

04

013

7E ndash

03

019

2E ndash

03

021

9E ndash

03

024

7E ndash

03

016

4E ndash

03

011

0E ndash

03

ZXY

MN



0

033

9E ndash

04

067

7E ndash

04

010

2E ndash

03

016

9E ndash

03

023

7E ndash

03

027

1E ndash

03

030

5E ndash

03

020

3E ndash

03

013

5E ndash

03

MN ZXY

0

032

9E ndash

04

065

7E ndash

04

098

6E ndash

04

016

4E ndash

03

023

0E ndash

03

026

3E ndash

03

029

6E ndash

03

019

7E ndash

03

013

1E ndash

03

MN ZXY







01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(a)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(b)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(c)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(d)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(e)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(f )


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(g)












ndash05

ndash04

ndash03

ndash02

ndash01

0

01

02

03

04

05

Disp

lace

men

t (m

)

10 20 30 40 50 60 700Time (s)



times106

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

5

Bend

ing

mom

ent (

kNmiddotm

)

10 20 30 40 50 60 700Time (s)









F(δ)

K1 K1 K1

K2

K2

δ

Fy






















Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Sa(T)


SAmax 01 sleTltTg

SAmaxTg

T1113874 1113875

c

Tg leTlt 10 s

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)








X







0

014

3E ndash

04

028

6E ndash

04

042

9E ndash

04

071

5E ndash

04

010

0E ndash

03

011

4E ndash

03

012

9E ndash

03

085

8E ndash

04

057

2E ndash

04

ZXY

MX

MN

0

027

4E ndash

04

054

8E ndash

04

082

2E ndash

04

013

7E ndash

03

019

2E ndash

03

021

9E ndash

03

024

7E ndash

03

016

4E ndash

03

011

0E ndash

03

ZXY

MN



0

033

9E ndash

04

067

7E ndash

04

010

2E ndash

03

016

9E ndash

03

023

7E ndash

03

027

1E ndash

03

030

5E ndash

03

020

3E ndash

03

013

5E ndash

03

MN ZXY

0

032

9E ndash

04

065

7E ndash

04

098

6E ndash

04

016

4E ndash

03

023

0E ndash

03

026

3E ndash

03

029

6E ndash

03

019

7E ndash

03

013

1E ndash

03

MN ZXY







01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(a)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(b)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(c)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(d)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(e)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(f )


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(g)












ndash05

ndash04

ndash03

ndash02

ndash01

0

01

02

03

04

05

Disp

lace

men

t (m

)

10 20 30 40 50 60 700Time (s)



times106

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

5

Bend

ing

mom

ent (

kNmiddotm

)

10 20 30 40 50 60 700Time (s)









F(δ)

K1 K1 K1

K2

K2

δ

Fy






















Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0

014

3E ndash

04

028

6E ndash

04

042

9E ndash

04

071

5E ndash

04

010

0E ndash

03

011

4E ndash

03

012

9E ndash

03

085

8E ndash

04

057

2E ndash

04

ZXY

MX

MN

0

027

4E ndash

04

054

8E ndash

04

082

2E ndash

04

013

7E ndash

03

019

2E ndash

03

021

9E ndash

03

024

7E ndash

03

016

4E ndash

03

011

0E ndash

03

ZXY

MN



0

033

9E ndash

04

067

7E ndash

04

010

2E ndash

03

016

9E ndash

03

023

7E ndash

03

027

1E ndash

03

030

5E ndash

03

020

3E ndash

03

013

5E ndash

03

MN ZXY

0

032

9E ndash

04

065

7E ndash

04

098

6E ndash

04

016

4E ndash

03

023

0E ndash

03

026

3E ndash

03

029

6E ndash

03

019

7E ndash

03

013

1E ndash

03

MN ZXY







01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(a)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(b)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(c)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(d)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(e)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(f )


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(g)












ndash05

ndash04

ndash03

ndash02

ndash01

0

01

02

03

04

05

Disp

lace

men

t (m

)

10 20 30 40 50 60 700Time (s)



times106

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

5

Bend

ing

mom

ent (

kNmiddotm

)

10 20 30 40 50 60 700Time (s)









F(δ)

K1 K1 K1

K2

K2

δ

Fy






















Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(a)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(b)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(c)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(d)


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(e)

10 20 30 40 50 60 700Time (s)


01234

Acce

lera

tion

(ms

2 )

(f )


01234

Acce

lera

tion

(ms

2 )

10 20 30 40 50 60 700Time (s)

(g)












ndash05

ndash04

ndash03

ndash02

ndash01

0

01

02

03

04

05

Disp

lace

men

t (m

)

10 20 30 40 50 60 700Time (s)



times106

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

5

Bend

ing

mom

ent (

kNmiddotm

)

10 20 30 40 50 60 700Time (s)









F(δ)

K1 K1 K1

K2

K2

δ

Fy






















Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











ndash05

ndash04

ndash03

ndash02

ndash01

0

01

02

03

04

05

Disp

lace

men

t (m

)

10 20 30 40 50 60 700Time (s)



times106

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

5

Bend

ing

mom

ent (

kNmiddotm

)

10 20 30 40 50 60 700Time (s)









F(δ)

K1 K1 K1

K2

K2

δ

Fy






















Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








F(δ)

K1 K1 K1

K2

K2

δ

Fy






















Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












Elastic cablesystem



Car + train



Temperatureaction



Seismicexcitations





























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























Viscous damper

Main girder

Viscous damper


(a)


Main girder



(b)


04

05

06

07

08

09

1

0806

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


04

05

06

07

08

09

1

081

06

0402

1000 2000 3000 4000


Velocity index α

Disp

lace

men

t (m

)

5000 6000


40004200440046004800

540052005000

0806

0402

1000 2000 3000 4000


Velocity index α

Bend

ing

mom

enttimes

103

(kN

middotm)

5000 6000


02

03

04

05

06

09

08

07

0806

0402

1000 2000 3000 4000


Velocity index α

Seism

ic st

roke

(m)

5000 6000










Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









Brak

ing

forc

e (kN

)

Time (s)6

025W

020W

015W

010W

005W

000W1881

a = 020g

a = 010g



0 10 20 30 40 50Time (s)

ndash3

ndash25

ndash2

ndash15

ndash1

ndash05

0

05

1

Def

orm

atio

n (m

)

times10ndash3

X 189 Y ndash0002521








6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







6 Conclusions




0 10 20 30 40 50Time (s)

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

Fric

tiona

l for

ce (k

N)

X 189 Y ndash1021


0 10 20 30 40 50Time (s)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

25

Bend

ing

mom

ent (

kNmiddotm

)

times104 X 1892Y 2241e + 04










Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Data Availability




p2 p1p3pi

155m 155m148m 148m 148m 148m

l2

lil3



0 10 20 30 40 50Time (s)

ndash3

ndash2

ndash1

0

1

2

3

4

Disp

lace

men

t (m

)

times10ndash3


X 178Y 0003832



0 10 20 30 40 50Time (s)

ndash200

ndash100

0

100

200

300

400

Dam

ping

forc

e (kN

)

X 1738Y 3617



Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


optimisationoflongitudinalseismicenergydissipation...

Documents