轨道结构空间振动时变模型建立方法的研究

A Study on the Method of Establishing the Spatial Vibration Model for Railway Tracks

基于既有的轨道模型,采用有限单元法,运用弹性系统总势能不变值原理及形成矩阵的"对号入座"法则,建立了轨道结构空间振动的振动方程组。采用轨道不断"增加和缩减"技术,使该模型的质量矩阵、阻尼矩阵、刚度矩阵和荷载列阵具有时变特性,从而便于计算无限长轨道上的车辆-轨道耦合振动。以法国TGV中速动车为例,速度取200km/h,计算了12km轨道上的车辆-轨道耦合振动动力响应值,列出了部分响应曲线图。该模型的建立为开展长时间的车辆-轨道耦合随机振动奠定了基础。

A new way to establish the time-dependent model of railway track spatial vibration is presented in this paper. Based on the existing track model and by using finite element method, equations of track spatial vibration are established following the principle of stationary total potential energy in elastic system dynamics and the 'set-in-right-position' rule for formulating matrix. By using the method of track being 'added and cut down', the mass matrix, damp matrix, stiffness matrix and force vector in the model become time-dependent and therefore it could be applied to the research of the vehicle-track coupling vibration with the length of track being limitless. As an example, the dynamic responses are calculated with a TGV middle-speed locomotive running at a speed of 200 kilometers per hour on the track of 12 kilometers and some typical response figures are listed at the end of the paper. The establishment of the model has laid a foundation for the research of the long-time vehicle-track coupling stochastic vibration.