几类非线性系统平稳随机响应的概率密度

THE PROBABILITY DENSITY FUNCTIONS OF THE STATIONARY RESPONSE OF CERTAIN CLASSES OF NONLINEAR SYSTEMS TO STOCHASTIC EXCITATION

本文考虑非保守力依赖于系统能量的非线性系统,构造了四类这种系统对白噪声外激与/或参激的平稳响应的精确概率密度,讨论了存在平稳响应的条件。同时指出,迄今为止已有的非线性系统平稳随机响应的精确解皆属本文给出一般结果的特殊情形。最后还给出几个例子说明一般结果。

In the present paper the nonlinear systems with energy-dependent nonconserva-tive forces are considered. The exact probability density functions of the stationary response of four classes of such systems to white noise external and/or parametric excitations are constructed. The conditions under which the steady-state solution exists are discussed. It is pointed out that all the steady-state solutions available up to now are special cases of the present solutions. Several examples are also given to illustrate the general results.