铁路车桥耦合振动模态法分析

Coupling vibration analysis of vehicle-bridge by mode method

以钢桁梁桥自由振动的模态和正则坐标作为桥跨结构振动的位移函数,将列车-钢桁梁桥作为一个系统,计算正则坐标下钢桁梁桥及车辆的总势能.基于弹性系统的总势能值不变原理及形成矩阵的对号入座法则,建立了车桥时变系统在正则坐标下的振动方程,有效减少了车桥振动的自由度和计算工作量.以某铁路为例,计算了连续钢桁梁桥车桥系统的振动响应,并用模态法和非模态法进行对比,最小误差为0.16%.

The free vibration mode of the truss girder bridge and normal coordinates are taken as displacement functions of the bridge vibration.By coupling the vehicle and the truss girder bridge as one composite system,the total potential energy of the vehicle and the truss girder bridge under normal coordinates are calculated.Based on the principle of the total potential energy with stationary value in elastic system and the set-in-right-position rule for forming structural matrices,the vibration equations of vehicle-bridge are established in time-varying system.The calculation results are compared with the ones by non-mode method.The minimum error of the results by the two methods is 0.16%.The mode method could reduce the degrees of freedom of the vehicle-bridge system,thus it reduces the computing time considerably.