基于Duhamel积分的车桥耦合动力分析方法

为了缩短求解车桥耦合系统动力响应的计算时间，利用振型分解法对车桥耦合系统的桥梁子系统和车辆子系统解耦，假定在每一时间步长内车桥相互作用力线性变化，借助Duhamel积分解析解，通过迭代得到系统的动力响应，提出了一种新型的车桥耦合动力分析方法.以一节四轴客车匀速通过32 m简支梁为例进行了实验研究，结果表明:本文方法得到的车桥耦合系统的动力响应结果与Newmark-β方法的结果接近，各极值点相对误差均不超过1%；在保证相同的计算精度前提下，本文方法将积分步长提高至原来的5~10倍，提高了求解速度. 

Analytical Method for Calculating Dynamic Response of Coupled Train-Bridge System Based on Duhamel Integral

In order to shorten the computation time of solving the dynamic response of a coupled train-bridge system, the modal decomposition method is used to decompose the train subsystem and bridge subsystem in the coupled system. Assuming that the vehicle-bridge interaction forces change linearly within each time step, the dynamic response of the system during this period is obtained by Duhamel integral. Based on this theory, a new method is proposed to analyze the dynamic response of the coupled train-bridge system. The proposed method is then used to analyze a 4-axle train passing through a 32 m simply-supported beam at a constant speed. The results show that the dynamic responses obtained by the proposed method for the coupled train-bridge system are very close to those obtained by the Newmark-β method, and the relative error at every extreme points is less than 1%. Compared with the Newmark-β method, the proposed method can increase the time interval of integration by at least 5-10 times while ensuring the precision.