拱桁组合体系桥车桥振动分析的模态法

摘要

首先计算出拱桁组合体系桥梁的自振特性,以桥梁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-桥梁作为一个系统,计算出在正则坐标下的桥梁结构及车辆的总势能.基于弹性系统动力学总势能不变值原理及形成矩阵的"对号入座"法则,建立并求解车桥时变系统在正则坐标下的空间振动方程(一个方程组,而不是车桥各自独立的两个方程组),分别计算桥梁结构的20、40、60和90阶振型.计算货物列车以80km/h速度的通过某拱桁组合体系桥梁的车桥系统的振动响应并与非模态法的计算结果对比,最小误差为0.17%.%The free vibration characteristics of the arch-truss composite bridge are calculated. Then, taking the free vibration modes of the bridge and normal coordinates as displacement functions of the bridge vibration, and the vehicle and the bridge as a system, the total potential energy of the vehicle and bridge structure under normal coordinates is calculated.Based on the principle of the stationary total potential energy in elastic system and the coding method for forming structural matrices, the vibration equations of vehicle-bridge time-varying system are established and solved. The former 20, 40, 60 and 90 order vibration modes of the bridge structure are calculated. The vehicle-bridge vibration responses of the truss-arch composite system are calculated when goods trains pass through the bridge at the speed of 80 km/h. The results are compared with those by using non-mode method. The minimum error is 0.17 ％ only.