迟滞系统受随机激励的响应计算

首先为随机激励设计了具有较高精度的滤波器，把迟滞系统受有色噪声激励的随机振动问题转化为由迟滞系统与滤波器组成的扩阶系统受白噪声激励的随机振动问题，然后详细论述了等效线性化法对此问题的具体求解，着重推导了高斯随机变量联合矩的递推关系和李亚普诺夫方程解法的实现，最后根据数字模拟结果分析了等效线性化法的精度和误差来源，给出了迟滞减振系统参数设计的有关建议。

The Response Calculation of Hysteretic Systems Under Random Excitation

First, a filter of rather high precision is designed for random excitation. The random vibration problem of a hysteretic system excited by colored noise is transformed into that of the extended system, consisting of hysteretic system and the filter, excited by white noise. Then the concrete solution to this problem by the method of equivalent linearization is elaborated. Recurrence relations about the joint moment of Gauss random variable and implement of solution for Liapunov equation are deduced emphatically. Finally, according to the result of digital simulations, the accuracy and error source of the method of equivalent linearization are analyzed, and some advice for parameter design of hysteretic vibration reduction systems is provided.