一种单自由度体系解析解及其在车桥动力分析中的应用

假定相邻时刻之间荷载线性变化,推导出低阻尼单自由度振动体系的解析解,在此基础上给出了相应的车桥动力相互作用系统建模及求解流程。系统模型分解为车辆、桥梁两个子系统,基于部件刚体假定和达朗贝尔原理推导车辆子系统运动方程,采用有限元法建立桥梁子系统模型;借助于振型叠加法将两个子系统运动方程解耦,车辆子系统非正交阻尼部分的影响以及两个子系统间的动力相互作用均按非线性虚拟力处理;以一节4轴客车匀速通过32 m简支梁为例,分别采用提出的解析解法、Newmark-β法以及高斯精细积分法进行动力分析。结果表明,相对于Newmark-β法和高斯精细积分法,解析解法不仅具有高精度特点,能显著提高计算收敛的积分步长,同时又能避免计算复杂的指数矩阵,具有良好的工程适用性。

Analytical solution to a sdof system and its application in dynamic analysisof a train-bridge system

With the assumption that a load varies linearly within each time step,an analytical solution was derived for a single-degree-of-freedom(SDOF) vibration system with low damping.Based on this solution,the modeling of a train-bridge system and its solving procedure were deduced.The train-bridge system model consisted of a train subsystem and a bridge one.The motion equation of the train subsystem was derived using the rigid component assumption and D′Alembert’s principle,and that of the bridge subsystem was derived using the finite element method.The mode superposition method was applied to uncouple the equations of motion of the two subsystems.The effects of the non-orthogonal damping of the train subsystem and the dynamic interaction between two subsystems were treated as nonlinear virtual forces.A 4-axle vehicle passing through a simply-supported beam of 32 m span at a constant speed was taken as a case study.The dynamic analysis of the coupled system was performed using the proposed analytical method,Newmark-β method and Gauss precise integration method,respectively.The results showed that compared with Newmark-β method and Gauss precise integration method,the analytical method can not only improve the time step of numerical integration but also avoid the computation of complex exponential matrices,so it has a good applicability in engineering.