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推广虚拟激励法来研究水平地震作用时三维车桥耦合时变系统的非平稳随机振动以及最大值估计方法。水平地震动假设为均匀调制非平稳随机过程;轨道不平顺假设为多点异相位均匀调制非平稳随机激励。借助时变系统的虚拟激励法将水平地震和轨道不平顺随机激励分别转化为一系列确定性简谐激励,为了能更真实地模拟车轮作用力在时间域和空间域的连续变化,采用精细积分格式进行数值积分,得到了系统随机响应的时变功率谱密度函数和标准差。最后基于首次穿越破坏准则给出了系统非平稳随机响应的最大值估计方法。在数值算例中,通过多样本时间历程法的统计平均验证了该文随机振动分析方法的正确性和最大值估计方法的有效性;并讨论了场地土条件对系统随机响应的影响。
The Virtual Excitation Method is extended to study the nonstationary random vibration and maximum estimation method of three-dimensional vehicle-bridge coupled time-varying system under horizontal seismic action. The horizontal ground motions are assumed to be uniformly modulated non-stationary stochastic processes. The track irregularity is assumed to be multi-point out-of-phase uniformly modulated non-stationary stochastic excitation. In order to simulate the continuous changes of wheel forces in the time and space domains with the help of the time-varying system’s virtual excitation method, the horizontal earthquake and the track irregularity random excitation are transformed into a series of deterministic harmonic excitation. Format of numerical integration, the system has been random response time-varying power spectral density function and standard deviation. Finally, based on the first pass through damage criterion, the maximum value estimation method of nonstationary random response of the system is given. In the numerical examples, the correctness of the stochastic vibration analysis method and the effectiveness of the maximum value estimation method are validated through the statistical averaging of multiple sample time history methods. The effect of site soil conditions on the random response of the system is also discussed.