Abstract: Vehicles and bridge oscillation equations were built respectively according to d’Alembert theory and finite element theory.The displacement of the bottom contact points of tires can be got from bridge nodal displacement by applying shape function interpolation.Then the contact point force which is equivalent to bridge unit nodes force was put into the bridge vibration equation and thus overall vibration equation of vehicle-bridge coupling vibration combing both vehicles and bridge oscillation equations was formed.In addition,Newmark-β method of numerical integration was applied to solve the equations.The result shows that this method and the classic iteration method are identical.

Key words: vehicles-bridge vibration, simultaneous equations, Newmark-β method

摘要： 根据d’Alembert 原理和有限元理论，分别建立了车辆和桥梁的振动方程； 基于车辆密贴理论，轮底接触点位 移由桥梁节点位移采用形函数插值得到，接触点作用力等效成桥梁单元的结点力代入桥梁振动方程，将车辆、桥梁 振动方程组联立形成了车-桥耦合振动的总体振动方程； 采用数值积分的Newmark-β 法求解方程组。结果表明: 此 方法和经典的迭代求解方法是吻合的。

关键词: 车桥振动, 联立方程, Newmark-β法