车-桥系统耦合振动响应的简便计算

依据振动理论推导出了二自由度模型车辆与桥梁系统竖向耦合振动微分方程，采用模态分析的离散化方法，将复杂的偏微分方程问题转化为变系数常微分方程问题，并将微分方程数值积分的Runge-Kutta方法引入到该时变系统的振动响应计算中，使复杂的耦合响应问题得到简便的解决。通过算例验证了该方法的有效性和简便性。该方法只需要直接数值积分，具有公式简单，编程方便，计算速度快等优点，特别适合于工程实际问题的计算，并且不仅适用于匀速运动车辆，也适用于变速运动车辆。

A Simple Numerical Calculation for Coupled Vibration Responses of a Vehicle-bridge System

By using the vibration theory, the vertical coupled vibration differential equations of a two-degree of freedom vehicle and bridge system are derived. By means of modal analysis, the complicated partial differential equations are transformed into common differential equations.The complicated coupled dynamics responses of the time-variant system can be obtained numerically by Runge-Kutta method. The numerical examples show that the method is accurate enough and efficient.The method has many advantages, such as simple in formulation, easy programing, and fast in computation. Both the method and the results presented here may be helpful in dealing with more complicated practical vibration problems. In particular, the method can be used when vehicle moves in constant speed or in variant speed.