车辆-轨道-桥梁系统竖向运动方程的建立

Formulation of Equations of Vertical Motion for Vehicle-track-bridge System

视车辆、轨道和桥梁为整个系统,将车辆模拟为由弹簧和阻尼器连接的多刚体,钢轨和桥梁均模拟为Bernoulli Euler梁,钢轨和桥梁之间的钢轨基础用连续的弹簧和阻尼器模拟。应用弹性系统动力学总势能不变值原理和形成矩阵的"对号入座"法则,建立了4轴双层悬挂系统车辆的车辆 轨道 桥梁单元和系统的竖向运动方程。与传统的方法(分别建立车辆运动方程,轨道和桥梁运动方程,这两种方程通过轮轨相互作用力耦合)相比,该方法能直接得到车辆 轨道 桥梁单元和系统的运动方程。举例说明了轨道表面不平顺对车辆、钢轨、桥梁以及车辆与钢轨之间接触力的动力响应的影响。

Vehicle, track and bridge are considered as an entire system. The vehicle is modeled as a multi-rigid body connected by springs and dampers. The rails and the bridge are each modeled as a Bernoulli-Euler beam, while the elasticity and damping properties of the rails bed are represented by continuous springs and dampers. For a four-axle vehicle having a two-layer suspension system, the equations of vertical motion for a vehicle-track-bridge element or system are formulated by means of the principle of total potential energy with a stationary value in elastic system dynamics and the 'set-in-right-position' rule for formulating matrices. Compared with the classical method that two sets of equations of motion are set up separately each for the two subsystems, one is the vehicle and the other is the track and bridge, and these two sets of equations are coupled by the interaction forces existing at the contact points, the proposed method can set up directly the equations of motion for a vehicle-track-bridge element or system. Numerical examples are given to illustrate the effect of track profile irregularity on dynamic responses of the vehicle, of the rails, of the bridge and of contact forces between the vehicle and the rails.