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Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

邮发代号 80-968

2019 Impact Factor: 1.68

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Frontiers of Structural and Civil Engineering  2016, Vol. 10 Issue (1): 81-92   https://doi.org/10.1007/s11709-015-0306-x
  本期目录
Vehicle-bridge coupled vibrations in different types of cable stayed bridges
Lingbo WANG1,*(),Peiwen JIANG2,Zhentao HUI3,Yinping MA1,Kai LIU4,Xin KANG5
1. Key Laboratory for Bridge and Tunnel of Shaanxi Province, Chang’an University, Xi’an 710064, China
2. Basic Construction Project Quality Supervision Station, Shaanxi Provincial Transport Department, Xi’an 710075, China
3. Yulin TianYuan Lu Ye Limited Company, 25 Shangjun Road, Yuyang District, Yulin 719000, China
4. School of Transportation Engineering, Hefei University of Technology, Hefei 230009, China
5. Department of Civil, Architectural, and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA
 全文: PDF(2505 KB)   HTML
Abstract：

Numerical analyses of the coupled vibrations of vehicle-bridge system and the effects of different types of cable stayed bridges on the coupled vibration responses have been presented in this paper using ANSYS. The bridge model and vehicle model were independently built which have no internal relationship in the ANSYS. The vehicle-bridge coupled vibration relationship was obtained by using the APDL program which subsequently imposed on the vehicle and bridge models during the numerical analysis. The proposed model was validated through a field measurements and literature data. The judging method, possibility, and criterion of the vehicle-bridge resonance (coupled vibrations) of cable stayed bridges (both the floating system and half floating system) under traffic flows were presented. The results indicated that the interval time between vehicles is the main influence factor on the resonance excitation frequency under the condition of equally spaced traffic flows. Compared to other types of cable stayed bridges, the floating bridge system has relatively high possibility to cause vehicle-bridge resonance.
Key words： vehicle-bridge coupled vibration    cable stayed bridge    resonances of vehicle-bridge system
收稿日期: 2014-12-31      出版日期: 2016-01-19
Corresponding Author(s): Lingbo WANG   
 引用本文:   
. [J]. Frontiers of Structural and Civil Engineering, 2016, 10(1): 81-92.
Lingbo WANG,Peiwen JIANG,Zhentao HUI,Yinping MA,Kai LIU,Xin KANG. Vehicle-bridge coupled vibrations in different types of cable stayed bridges. Front. Struct. Civ. Eng., 2016, 10(1): 81-92.
 链接本文:  
https://academic.hep.com.cn/fsce/CN/10.1007/s11709-015-0306-x
https://academic.hep.com.cn/fsce/CN/Y2016/V10/I1/81
bridge parameters vehicle parameters
span /m linear density /(kg·m−1) bending stiffness /(N·m2) suspension system mass (m1/kg) vehicle mass (m2/kg) spring stiffness (k/N·m−1) spring damping (c/kg·s−1)
16 9.36x103 2.05x1010 4.69x104 1.69x104 4.87x106 3.14x105
Tab.1  
Fig.1  
vehicle reaching moment FEA analysis vehicle leaving moment
1 Before vehicle load acting on the bridge, initial state U0(i), V0(i) and A0(i) were given or set static as its initial statevehicle model: free vibration under initial state;bridge model: static substep interval Δt, total time Δt,transient analysis Calculating results of bridge node: U1(i) = 0, V1(i) = 0, A1(i) = 0, i = 1−101;Calculating results of vehicle node: U1(i), numerical differentiation was used to obtain: V1(i) and A1(i)V1(i) = (U1(i)- U0(i))/ΔtA1(i) = (V1(i)- V0(i))/Δti = 201~202
2 Assume that there is no displacement at the No. 2 node for its short distance from the support.Interaction force was applied on bridge node No. 2: F = k ( U 1 ( 2 ) - U 1 ( 202 ) ) + c ( V 1 ( 2 ) - V 1 ( 202 ) ) + m 1 A 1 ( 2 ) + m 1 g substep interval Δt, total time 2Δt,transient analysis U2(i) were obtainedsimilarly:V2(i) = (U2(i)- U1(i))/ΔtA2(i) = (V2(i)- V1(i))/Δti = 1~101,201,202
3 Vehicle model: vertical displacement U2 (3) was applied on bottom node of vehicle model based on consistency in deformation between vehicle wheel and bridgeInteraction force was applied on bridge node No. 2: F = k ( U 2 ( 3 ) - U 2 ( 202 ) ) + c ( V 2 ( 3 ) - V 2 ( 202 ) ) + m 1 A 2 ( 3 ) + m 1 g substep interval Δt, total time 3Δt,transient analysis U3(i) were obtainedsimilarly:V3(i) = (U3(i)- U2(i))/ΔtA3(i) = (V3(i)- V2(i))/Δti = 1~101,201,202
j Similarly, vertical displacement Uj-1(j) was applied on bottom node of the vehicle modelInteraction force was applied on bridge node No. i: F = k ( U j − 1 ( j ) - U j − 1 ( 202 ) ) + c ( V j − 1 ( j ) - V j − 1 ( 202 ) ) + m 1 A j − 1 ( j ) + m 1 g substep interval Δt,total time i*Δt,transient analysis Ui(i) were obtainedsimilarly:Vj(i) = (Uj(i)- Uj-1(i))/ΔtAj(i) = (Vj(i)- Vj-1(i))/Δti = 1~101,201,202
Tab.2  
Fig.2  
Fig.3  
Fig.4  
Fig.5  
floating system half floating system (fixed support) half floating system (none fixed support) rigid system
first mode frequency 0.191 0.603 0.191 0.617
second mode frequency 0.604 0.673 0.605 0.704
third mode frequency 0.825 0.825 0.938 1.269
Tab.3  
Fig.6  
Fig.7  
Fig.8  
Fig.9  
Fig.10  
Fig.11  
Fig.12  
conditions vehicle arrangements structure system vehicle velocity/(km/h) vehicle basal frequency/Hz interval time of vehicle/s frequency of traffic flow/Hz bridge frequency /Hz judging results of the presented method
condition 1 single vehicle floating system 60,120 0.198 / / 0.191 none resonance
condition 2 single vehicle half floating system(horizontal restraint) 60,120 0.198 / / 0.603 none resonance
condition 3 single vehicle half floating system(none horizontal restraint) 60,120 0.198 / / 0.191 none resonance
condition 4 single vehicle rigid system 60,120 0.198 / / 0.617 none resonance
condition 5 10 vechileequally spaced floating system 60,120 0.198 5s 0.2 0.191 resonance
condition 6 10 vechileequally spaced half floating system(horizontal restraint) 60,120 0.198 5s 0.2 0.603 none resonance
condition 7 10 vechileequally spaced half floating system(none horizontal restraint) 60,120 0.198 5s 0.2 0.191 resonance
condition 8 10 vechileequally spaced rigid system 60,120 0.198 5s 0.2 0.617 none resonance
condition 9 10 vechileequally spaced floating system 120 0.198 2.5s,10s 0.4,0.1 0.191 none resonance/resonance weakened
condition 10 10 vechilerandom spaced floating system 60 0.198 Random 2-7s / 0.191 none resonance
Tab.4  
Fig.13  
Fig.14  
Fig.15  
Fig.16  
Fig.17  
Fig.18  
Fig.19  
Fig.20  
Fig.21  
Fig.22  
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