分析非线性随机结构动态响应的等效随机系统法

在确定性非线性系统等效线性化方法的基础上，提出了分析含有随机参数的非线性结构动态响应的等效随机系统法。考虑了最一般的多自由度系统，以刚度随机为例推导了等效随机系统法的公式，并给出等效随机系统法的算法。以非线性单自由度系统为算例进行计算，结果表明，等效随机系统法得到的解与Monte—Carlo模拟解几乎完全吻合。本方法精度较高，且与Monte—Carlo法相比计算时间大大缩短。

A equivalent random system method for analyzing response of nonlinear structures with uncertain physical parameters

There are many research papers about mathematic theory of stochastic course and stochastic differential equation, but no a whole theory can be used to analyse nonlinear system. On the base of equivalent linearization method about certain nonlinear system, a equivalent random systems method was developed and used in analyzing the dynamic response of nonlinear random structures. Considering the multi-degree of freedom system, the formula of equivalent random systems method was expounded. The nonlinear mono-degree of freedom system was taken for example. The numerical results showed that the responses of the proposed approach were much close to the Monte-Carlo solutions, and the time used in computing was much less than the Monte-Carlo mothed.