几类非线性系统对白噪声参激与/或外激平稳响应的精确解<sup>*</sup>

朱位秋

几类非线性系统对白噪声参激与/或外激平稳响应的精确解^*

朱位秋

浙江大学

基金项目: * 国家自然科学基金资助项目

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出版历程
- 收稿日期: 1988-10-31
- 刊出日期: 1990-02-15

Exact Solutions for Stationary Responses of Several Classes of Nonlinear Systems to Parametric and/or External White Noise Excitations

Zhu Wei-qiu

Dept. of Mechanics, Zhejiang University, Hangzhou

摘要

摘要: 用福克-普朗克-柯尔莫哥洛夫方程方法构造了一类二阶、三类高阶非线性系统对白噪声参激与/或外激的平稳响应的精确解.讨论了解的存在与唯一性及解的性态.所考虑的系统的共同特点是非保守力依赖于相应保守系统的首次积分,因此可称为广义能量依赖系统.文中指出,对每个广义能量依赖系统,存在一族与之随机等价的非广义能量依赖系统,它们有相同的平稳概率密度.并指出对一给定广义能量依赖系统,如何找到其等价随机系统.作为例子,给出了二阶广义能量依赖随机系统的等价随机系统.最后指出并用例子说明,许多非广义能量依赖非线性随机系统的精确平稳解可通过寻求其等价广义能量依赖系统而找到.

Abstract: The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-Planck-Kolmogorov et/ualion approach.The conditions for the existence and uniqueness and the behavior of the solutions are discussed.All the systems under consideration are characterized by the dependence ofnonconservative fqrces on the first integrals of the corresponding conservative systems and arc catted generalized-energy-dependent f G.E.D.) systems.It is shown taht for each of the four classes of G.E.D.nonlinear stochastic systems there is a family of non-G.E.D.systems which are equivalent to the G.E.D.system in the sense of having identical stationary solution.The way to find the equivalent stochastic systems for a given G.E.D.system is indicated and.as an example,the equivalent stochastic systems for the second order G.E.D.nonlinear stochastic system are given.It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D.nonlinear stochastic systems may he found by searching the equivalent G.E.D.systems.

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参考文献(10)

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