基于有限元和Duhamel积分的移动力问题分析方法研究

朱丹阳; 张亚辉

doi:10.3879/j.issn.1000-0887.2014.12.001

基于有限元和Duhamel积分的移动力问题分析方法研究

doi: 10.3879/j.issn.1000-0887.2014.12.001

工业装备结构分析国家重点实验室(大连理工大学), 辽宁大连 116024

基金项目: 国家自然科学基金（11172056）；国家重点基础研究发展计划(973计划)（2014CB046803）

详细信息

作者简介:
朱丹阳（1985—），男，湖南郴州人，博士生（E-mail: zhudy@mail.dlut.edu.cn）;张亚辉（1972—），男，河北昌黎人，教授，博士生导师（通讯作者. E-mail: zhangyh@dlut.edu.cn）.

中图分类号: O326
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出版历程
- 收稿日期: 2014-10-08
- 修回日期: 2014-10-21
- 刊出日期: 2014-12-15

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

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）

摘要

摘要: 针对桥梁在移动力作用下的动力响应问题，提出了一种基于有限元模型和Duhamel积分的半解析分析方法，以此为基础，推导了多个移动力作用下桥梁动力响应的共振和相消条件.该方法基于桥梁有限元模型的振型，通过单元形函数构造桥面分段连续振型，得到Duhamel积分在任意桥面单元内的解析表达，将时间变量从被积函数中分离出去并利用积分的可加性，使得前面时刻的积分不必重复计算，因此每一个计算时间节点仅需计算一次简单积分和一次求和，这样极大地减少了计算时间.该方法在计算中未引入任何近似，且其精度与时间积分步长无关，是有限元模型下的解析解答.在数值算例中，分别针对简支梁和三跨连续桥梁，通过与解析解和Newmark法的对比，验证了该方法的精确性；然后针对多个移动力问题，验证了桥梁动力响应的共振和相消条件，探讨了载荷间距对复杂结构动力响应共振和相消的影响.
- 移动力 /
- 桥梁 /
- 有限元法 /
- 共振和相消
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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参考文献(18)

[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.

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基于有限元和Duhamel积分的移动力问题分析方法研究

doi: 10.3879/j.issn.1000-0887.2014.12.001

作者简介:
朱丹阳（1985—），男，湖南郴州人，博士生（E-mail: zhudy@mail.dlut.edu.cn）;张亚辉（1972—），男，河北昌黎人，教授，博士生导师（通讯作者. E-mail: zhangyh@dlut.edu.cn）.

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

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基于有限元和Duhamel积分的移动力问题分析方法研究

doi: 10.3879/j.issn.1000-0887.2014.12.001

作者简介: 朱丹阳（1985—），男，湖南郴州人，博士生（E-mail: zhudy@mail.dlut.edu.cn）;张亚辉（1972—），男，河北昌黎人，教授，博士生导师（通讯作者. E-mail: zhangyh@dlut.edu.cn）.

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出版历程

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

计量

出版历程

目录

作者简介:
朱丹阳（1985—），男，湖南郴州人，博士生（E-mail: zhudy@mail.dlut.edu.cn）;张亚辉（1972—），男，河北昌黎人，教授，博士生导师（通讯作者. E-mail: zhangyh@dlut.edu.cn）.