大规模非线性系统随机振动显式迭代Monte Carlo模拟法

Random vibration analysis of large-scale nonlinear systems by explicit iteration Monte Carlo simulation method

探讨了非平稳随机激励下大规模非线性系统随机振动Monte Carlo模拟法。引入等效激励的概念,把非线性系统动力方程写成状态方程的形式,并采用精细积分法对状态方程进行数值求解,导出非线性系统振动分析的显式迭代法。基于所导出的显式迭代公式,可以有效提高单次确定性非线性振动分析的计算效率,从而可以通过Monte Carlo模拟获得非平稳随机激励下非线性系统随机响应的统计信息,同时还可以获取非线性系统随机响应的演化概率密度函数。数值算例表明,所提出的方法迭代收敛速度快,计算精度高,适用于求解大规模非线性系统随机振动问题。

In the present paper, the Monte Carlo simulation method is investigated for the random vibration analysis of the large-scale nonlinear systems that is subjected to non-stationary random excitations. Motion equations of nonlinear systems are first transformed into the form of state equations by introducing the concept of equivalent excitations and solved by the precise time integration method. An explicit iteration expression is then deduced for dynamic response analysis of nonlinear systems. Based on the above explicit iteration expression, the computational cost for deterministic dynamic analysis of nonlinear systems can be significantly reduced, and therefore Monte Carlo simulation can be readily conducted using the explicit iteration expression as the tool for sample tests. Statistical properties of the non-stationary random response of a nonlinear system, including the evolutionary probability density function of the response, can be obtained with the proposed method. Numerical examples show that the present approach is of high accuracy and efficiency and is suitable for random vibration analysis of large-scale nonlinear systems.