A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads

ZHU Dan-yang; ZHANG Ya-hui

doi:10.3879/j.issn.1000-0887.2014.12.001

Volume 35 Issue 12

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ZHU Dan-yang, ZHANG Ya-hui. A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1287-1298. doi: 10.3879/j.issn.1000-0887.2014.12.001

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A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads

doi: 10.3879/j.issn.1000-0887.2014.12.001

State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology), Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China（11172056）;The National Basic Research Program of China (973 Program)（2014CB046803）

Received Date: 2014-10-08
Rev Recd Date: 2014-10-21
Publish Date: 2014-12-15

Abstract

Abstract

Based on the finite element (FE) method and Duhamel integration, a numericalanalytical combined method for the dynamic response problem of an FE bridge under moving loads was proposed, and the conditions of resonance and cancellation for the bridge subjected to multiple moving loads were derived. The FE modes of the bridge structure were first computed and then converted into an analytical form constructed over all the elements of the bridge deck with the element shape functions. The analytical dynamic responses of the bridge were derived from Duhamel integration, and transformed into a simple integration and a summation of the previous results through elimination of the time variable from the integration, which enables the computation process more efficient. The proposed approach has the versatility of the FE method in dealing with structures of arbitrary configurations and the special efficiency and convenience of the analytical method in dealing with moving loads. In the numerical examples, the present method is verified with the Newmark method and the traditional analytical method based on a simply supported beam bridge and a 3span continuous beam bridge. The results show that the accurate solution of the FE structures subjected to moving loads is obtained with the present method, and no approximation is introduced during the computation process. The conditions of resonance and cancellation are discussed for the problems with multiple moving load, and the influence of the load distances on the responses of the bridge is also revealed.
- moving load,
- bridge,
- finite element method,
- resonance and cancellation

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References(18)

References

[1]	Stokes G G. Discussions of a differential equation relating to the breaking of railway bridges[C]// Mathematical and Physical Papers.Vol2. Cambridge: Cambridge University Press, 2009: 178-220.(Original Publicated in 1883)
[2]	Tan C P, Shore S. Response of horizontally curved bridge to moving load[J].Journal of the Structural Division,1968,94(9): 2135-2151.
[3]	Ting E, Yener M. Vehicle-structure interactions in bridge dynamics[J].The Shock and Vibration Digest,1983,15(12): 3-9.
[4]	Frba L. Vibration of Solids and Structures Under Moving Loads [M]. Netherlands: Noordhoff International Publishing, 1972.
[5]	Olsson M. Finite element, modal co-ordinate analysis of structures subjected to moving loads[J].Journal of Sound and Vibration,1985,99(1): 1-12.
[6]	Olsson M. On the fundamental moving load problem[J].Journal of Sound and Vibration,1991,145(2): 299-307.
[7]	Baeza L, Ouyang H. Vibration of a truss structure excited by a moving oscillator[J].Journal of Sound and Vibration,2009,321(3): 721-734.
[8]	夏禾. 车辆与结构动力相互作用[M]. 北京: 科学出版社, 2002.(XIA He. Interaction Dynamics Between Vehicles and Structures[M]. Beijing: Science Press, 2002.(in Chinese))
[9]	Yang Y B, Yau J D, Hsu L C. Vibration of simple beams due to trains moving at high speeds[J].Engineering Structures,1997,19(11): 936-944.
[10]	Michaltsos G, Sophianopoulos D, Kounadis A N. The effect of a moving mass and other parameters on the dynamic response of a simply supported beam[J].Journal of Sound and Vibration,1996,191(3): 357-362.
[11]	Pesterev A V, Bergman L A. Response of elastic continuum carrying moving linear oscillator[J].ASCE Journal of Engineering Mechanics, 1997,123(8): 878-884.
[12]	Marchesiello S, Fasana A, Garibaldi L, Piombo B. Dynamics of multi-span continuous straight bridges subject to multi-degrees of freedom moving vehicle excitation[J].Journal of Sound and Vibration,1999,224(3): 541-561.
[13]	Xia H, Xu Y L, Chan T H T. Dynamic interaction of long suspension bridges with running trains[J].Journal of Sound and Vibration,2000,237(2): 263-280.
[14]	Green M F, Cebon D. Dynamic interaction between heavy vehicles and highway bridges[J].Computers & Structures,1997,62(2): 253-264.
[15]	Henchi K, Fafard M, Talbot M, Dhatt G. An efficient algorithm for dynamic analysis of bridges under moving vehicles using a coupled modal and physical components approach[J].Journal of Sound and Vibration,1998,212(4): 663-683.
[16]	张亚辉, 张守云, 赵岩, 宋刚, 林家浩. 桥梁受移动荷载动力响应的一种精细积分法[J]. 计算力学学报, 2006,23(3): 290-294.(ZHANG Ya-hui, ZHANG Shou-yun, ZHAO Yan, SONG Gang, LIN Jia-hao. A precise integration method for bridges subjected to moving loads[J].Chinese Journal of Computational Mechanics,2006,23(4): 290-294.(in Chinese))
[17]	Zhu D Y, Zhang Y H, Kennedy D, Williams F W. Stochastic vibration of vehicle-bridge system subject to non-uniform ground motions[J].Vehicle System Dynamics,2014,52(3): 410-428.
[18]	OUYANG Hua-jiang. Moving-load dynamic problems: a tutorial (with a brief overview)[J].Mechanical Systems and Signal Processing,2011,25(6): 2039-2060.