三维车桥耦合系统的非平稳随机振动分析

推导了线性时变系统非平稳随机响应的多维虚拟激励法,研究了三维车桥耦合系统受轨道激励而产生的非平稳随机振动。桥梁模型采用空间Euler梁单元,轨道激励假设为均匀调制多点异相位非平稳随机激励。采用多维虚拟激励法把轨道不平度转化为一系列简谐不平度的叠加,通过简单分解精细积分格式进行迭代计算,最终得到系统随机响应的时变功率谱及均方根。数值算例中,用时间历程法验证了本文方法的正确性,并且分析了方向、高低、水平三类轨道激励同时作用下三维车桥耦合系统的非平稳随机振动特性。

Non-stationary random vibration analysis of three-dimensional train-bridge systems

The multi-dimensional pseudo-excitation method for time-dependent systems is developed and applied to analyze the non-stationary random vibration of three-dimensional train-bridge systems subjected to track irregularities.Each vehicle is described by 27 degrees of freedom.The bridge deck is modeled as a three-dimensional Euler beam,and the track irregularities are assumed to be uniformly modulated multi-point different-phase non-stationary random excitations.Based on the multi-dimensional pseudo-excitation method,the random surface roughness of the track is transformed into the superposition of a series of deterministic pseudo harmonic surface unevenness.The responses of the time-variant coupled system due to each of such harmonic excitations are solved by the precise integration method through its simple decomposition format iteratively,and thus the time-dependent PSD and RMS of system responses are obtained conveniently and efficiently.The effectiveness and the accuracy of the present method are justified numerically by the time history method,and the characteristics of such non-stationary random vibration are discussed.