车-桥竖向随机振动响应的概率分析

视车辆、桥梁为一个系统,利用弹性系统的动力学总势能不变值原理和形成矩阵的"对号入座"法则建立了该系统的竖向运动方程。以德国高速谱为激励,得到系统的随机动力响应。将车辆每种运行速度下的车-桥动力响应最大值视为随机变量的1个样本值,通过统计分析,获得车-桥动力响应的概率特征,并探讨车辆速度对车-桥动力响应的影响规律。研究结果表明:车-桥动力响应的最大值随机变量均服从正态分布;随着车辆速度的增加,轮对与桥梁作用力最大值和车体加速度最大值的均值均增加,而桥梁中点的位移、加速度最大值的均值并不与之成正比。

Probability analysis for random vibration responses of vehicle-bridge system

The vehicle and bridge were considered as an entire system.The equations of vertical motion for the system were formulated based on the principle of total potential energy with a stationary value in elastic system dynamics and the "set-in-right-position" rule for formulating matrices.Based on the German high-speed spectrum for the excitation,the random dynamic responses of the system were obtained.The maximum dynamic response of the system at each speed was taken as a sample value of the random variable.The probability characteristics and distribution law of the dynamic responses were obtained by statistical analysis.Furthermore,the influences of the vehicle speed on the dynamic responses were explored.The results show that the random variables of the vehicle-bridge dynamic response maximum values fall into normal distribution.With the increase of the speed of vehicle,the mean of maximum wheel-bridge force and the acceleration of car body are both increased,but the mean of maximum bridge midpoint displacement and the acceleration of bridge midpoint do not increase.