交通运输工程学报
JOURNAL OF TRAFFIC AND TRANSPORTATION ENGINEERING
2003 Vol.3 No.2 P.1-6


移动荷载作用下连续粘弹性基础支承无限长梁的有限元分析

Finite element analysis of infinitely long beam resting on continuous viscoelastic foundation subjected to moving loads

娄平  曾庆元 

摘 要:把无限长梁、连续粘弹性基础和移动荷载视为一个系统,并将该系统进行有限单元离散,梁单元的弯曲形函数采用Hermitian三次方插值函数,利用弹性系统动力学总势能不变值原理,得到单元的刚度矩阵、质量矩阵、阻尼矩阵和节点荷载列阵,建立该系统的振动方程组;再用Wilson θ法求解该振动方程组,得到梁中点的位移时程曲线.举例分析了基础的粘弹性特性和梁的抗弯刚度对梁动力响应的影响.计算结果表明:增大基础的弹性系数、阻尼系数和梁的抗弯刚度都有利于减小梁的动力响应.
关键词:铁道工程;结构分析;有限单元法;变分原理;势能;移动荷载;粘弹性基础;无限长梁
分类号:U211.4;TB122  文献标识码:A

文章编号:1671-1637(2003)02-0001-06

基金项目:国家自然科学基金项目(50078006);铁道部科技研究开发计划项目(2001G029);教育部博士点基金项目(20010533004)
作者简介:娄平(1968-),男,湖南浏阳人,讲师,博士生,从事列车轨道(桥梁)振动、结构可靠度研究.
作者单位:娄平(中南大学,土木建筑学院,湖南,长沙,410075) 
     曾庆元(中南大学,土木建筑学院,湖南,长沙,410075) 

参考文献:

[1]Yoshida D M,Weaver W.Finite element analysis of beams and plates with moving loads[J].Publication of International Association for Bridge and Structural Engineering,1971,31(1):179-195.
[2]Filho F V.Finite element analysis of structures under moving loads [J].Shock and Vibration Digest,1978,10(8):27-35.
[3]Olsson M.Finite element,modal co-ordinate analysis of stru-ctures subjected to moving loads [J].Journal of Sound and Vibration,1985,99(1):1-12.
[4]Thambiratnam D,Zhuge Y.Dynamic analysis of beams on an elastic foundation subjected to moving loads[J].Journal of Sound and Vibration,1996,198(2):149-169.
[5]WU Jong-shyong,DAI Chang-wang.Dynamic responses ofmultispan nonuniform beam due to moving loads[J].Journal of Structural Engineering,1987,113(3):458-474.
[6]Clough R W,Penzien J.Dynamics of Structures[M].McGraw-Hill Inc.,New York,1975.
[7]Meirovitch L.Analytical Methods in Vibrations[M].Macmil-lan Company,London,U.K.,1967.
[8]Pilkey W D,Chang P Y.Modern Formulas for Statics and Dynamics [M].McGraw-Hill Book Co.,New York,1978.
[9]Cai C W,Cheung Y K,Chan H C.Dynamic response of infinite continuous beams subjected to a moving force - an exact method [J].Journal of Sound and Vibration,1988,123(3):461-472.
[10]Dean G Duffy.The response of an infinite railroad track to a moving,vibrating mass[J].Journal of Applied Mechanics,1990,57(1):66-73.
[11]郝瀛.铁道工程[M].北京:中国铁道出版社,2000.
[12]曾庆元.弹性系统总势能不变值原理[J].华中理工大学学报,2000,28(1):1-3.ZENG Qing-yuan.The principle of total potential energy with stationary value in elastic system dynamics [J].Journal of Huazhong University of Science and Technology,2000,28(1):1-3.(in Chinese).
[13]曾庆元,郭向荣.列车桥梁时变系统振动分析理论与应用[M].北京:中国铁道出版社,1999.
[14]曾庆元,杨平.形成矩阵的"对号入座"法则与桁梁空间分析的桁段有限元法[J].铁道学报,1986,8(2):48-59.ZENG Qing-yuan,YANG Ping.The "set-in-right-position" rule for forming structural matrices and the finite truss-element method for space analysis of truss bridges[J].Journal of the China Railway Society,1986,8(2):48-59.(in Chinese).
[15]ZENG Qing-yuan,LOU Ping,XIANG Jun.The principle of total potential energy with stationary value in elastic system dynamics and its application to the analysis of vibration and dynamic stability [J].Journal of Huazhong University of Science and Technology (Urban Science),2002,19(1):7-14.
[16]ZENG Qing-yuan,LOU Ping,XIANG Jun.The principle of total potential energy with stationary value in elastic system dynamics and its vibration analysis [A].Proceedings of International Conference on Engineering and Technological Sciences 2000,Session 5[C].Beijing:Science Press,2000.183-193.
[17]LOU Ping,ZENG Qing-yuan.On three approaches to formula-tion of the equations of motion of a dynamic system [J].Journal of Structural Engineering(Madras),2002,29(2):119-123.
[18]李德建.列车-轨道时变系统空间振动分析[D].长沙:长沙铁道学院,1996.
[19]郭文华.中小跨度铁路桥梁横向刚度分析[D].长沙:长沙铁道学院,1999.


收稿日期:2002年10月25日

出版日期:2003年6月1日