层状饱和地基－轨道－列车耦合系统轨道不平顺引起的振动分析

摘要

The dynamic responses of a layered saturated ground-track-train coupled system were studied with the semi-analytical method.The layered saturated ground was composed of arbitrary horizontal saturated layers and the underlying saturated half-space.The track was composed of rail,sleepers and ballasts.The rail was regarded as an infinitely long Euler beam,the sleepers were represented with continuous masses and the ballasts were accounted for by introducing Cosserat model.The vehicle was taken as a multi-rigid-body system with spring and damping elements being connecting parts.The vibration inputs were provided by rail vertical irregularities.The coupling between the layered saturated ground and the track was realized with the condition that the vertical displacement of the track center on the ground surface be equal to the displacement of the ballasts.The coupling between the track and the train was realized by introducing Hertzian contact springs between wheels and rail.The system's dynamic responses were firstly obtained in frequency-wave number domain and then were transformed into time-space domain with the inverse Fourier transformation. The correctness of the method was verified.The numerical calculation and analysis were performed.The study showed that for lower vibration frequencies induced by track irregularities,the ground surface displacement amplitudes increase gradually with increase in the velocity of the train,while for higher vibration frequencies,the maximum displacement amplitudes seem to be insensitive to the velocity of the train,but the ground vibrations are more serious and the vibration durations become longer after the train passing.%采用半解析方法研究了层状饱和地基－轨道－列车耦合系统的动力响应问题。层状饱和地基由任意水平饱和土层和下卧饱和半空间组成，轨道采用以无限长欧拉梁模拟的钢轨、连续质量块模拟的轨枕和 Cosserat 模型模拟的道砟组成的三层系统，列车模拟为弹簧和阻尼元件连接的多刚体系统。振动输入由钢轨的竖向不平顺提供。通过地基表面轨道中心处竖向位移与道砟位移相等实现层状饱和地基和轨道的耦合，通过在车轮与钢轨间引入 Hertizian 接触弹簧来实现轨道与列车的耦合，首先求得频率－波数域内解答，然后通过 Fourier 逆变换求得时间－空间域内振动响应。文中验证了方法的正确性，并进行了数值计算分析，研究表明钢轨不平顺引起的列车动荷载振动频率较低时，随着列车运行速度的增大地基表面位移幅值逐渐增大；振动频率较高时，列车运行速度对位移幅值峰值的影响不明显，但列车驶过后地基的振动明显增大，振动时间变长。