基于改进高斯精细积分法的车桥耦合振动分析框架  

DYNAMIC ANALYSIS FRAMEWORK OF TRAIN-BRIDGE SYSTEM BASED ON IMPROVED GAUSS PRECISE INTEGRATION METHOD

作　　者：杜宪亭[1] 夏禾[1] 李慧乐[1] 崔堃鹏[1] 

机构地区：[1]北京交通大学土木建筑工程学院,北京100044

出　　处：《工程力学》2013年第9期171-176,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(51208027);973计划项目(2013CB036203);中央高校基本科研业务费专项资金资助项目(C12JB00250)

摘　　要：假定任一时刻的位移可以根据其相邻时间步上的运动状态由Hermite插值函数确定,采用3节点高斯积分方法展开精细积分法中状态方程的Duhamel项,构造了一种改进的高斯精细积分算法用于求解结构非线性问题,在此基础上,提出了适用于车桥耦合振动研究的高效求解分析框架。车桥耦合系统由车辆、桥梁有限元子系统组成,其中车辆子系统引入部件刚体假定,而桥梁子系统借助于振型叠加法缩减自由度数目,两个子系统间的相互作用通过非线性的虚拟力表达。以一节4轴客车匀速通过32m简支梁为研究对象,分别采用所提出的分析框架、传统Newmark-β法进行动力分析。结果表明:相对于Newmark-β法,高斯精细积分方法既能避免求解线性方程组,又可显著提高计算收敛的积分步长,分析框架显示出良好的实用效果。With the assumption that the displacement of any moment can be determined by the motion of its two adjacent time steps with the help of a Hermite interpolating function, an improved Gauss precise integration method is constructed to solve the structural nonlinear problems, in which the Duhamel term of a state equation of a precise time-integration method is expanded in terms of 3-node Gauss integration method. On the basis of the improved method, an efficient analysis framework for the dynamic interaction analysis of a train-bridge system is proposed. The train-bridge system consists of train subsystems and bridge subsystems, and both of them are established with the finite element method. The rigid component assumption is introduced to the train subsystem, the mode superposition method is applied to the bridge subsystem to reduce the degrees-of-freedom, and the dynamic interaction between two subsystems is expressed with nonlinear virtual forces. A 4-axle vehicle passing through a simply-supported beam with a 32m span at constant speed is taken as a case study. The dynamic analysis of the coupled system is carried out by using the proposed framework and the traditional Newmak-β method, respectively. The numerical results show that the improved Gauss precise integration method not only avoids the solution of linear equations but also improves the time interval of integration, comparing withNewmak-β method, and the framework shows good effectiveness in application.

关 键 词：车桥耦合系统 动力分析 精细积分法 高斯积分法 振型叠加法 

分 类 号：U24[交通运输工程—道路与铁道工程]