非线性系统非平稳随机响应的时域模态分析法

Time Domain Modal Analysis for Non stationary Random Response of Non linear System

采用时域模态分析和统计线性化法，得到了一个计算非线性多自由度系统非平稳随机响应的方法。该方法是基于统计线性化参数在一系列微小时间间隔内保持不变，而在这些微小时间间隔的分界点突然改变的假定。考虑了等效线性化系统的时变性；获得了响应协方差矩阵的递推关系。给出了两个算例，并将计算结果与相应的数字模拟结果进行了比较。结果证明该方法是具有满意精度和有效。

By applying the time domain modal analysis and statistical linearization technique, a method for calculating the non stationary random response of non linear multi degree of freedom system is obtained in this paper. The statistical linearization parameters are assumed to vary in a stepwise way, i.e., they change abruptly at instants separated by small time intervals, and remain constant during these intervals. The time varying equivalent linearization system is considered and a recursive relation for evaluating the covariance matrix isobtained. Two examples are presented and computational results are compared with those of corresponding digital simulation. This method is effective, applicable to time varying systems with satisfactory accuracy.