## 留言板

 引用本文: 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*[J]. 应用数学和力学, 1990, 11(2): 155-164.
Zhu Wei-qiu. Exact Solutions for Stationary Responses of Several Classes of Nonlinear Systems to Parametric and/or External White Noise Excitations[J]. Applied Mathematics and Mechanics, 1990, 11(2): 155-164.
 Citation: Zhu Wei-qiu. Exact Solutions for Stationary Responses of Several Classes of Nonlinear Systems to Parametric and/or External White Noise Excitations[J]. Applied Mathematics and Mechanics, 1990, 11(2): 155-164.

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

• 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.
•  [1] Crandall,S.H.and W.Q.Zhu,Random vibration:A survey of recent developments,J.Appl.Mech.,50th Anniversary Volume,50(1983),953-962. [2] Caughey,T.K.,Nonlinear theory of random vibrations,Advances in Applied Mechanics,11(1971),209-253. [3] Roberts,J.B.,Response of nonlinear mechanical systems to random excitation,Part 1:Markov method,The Shock and Vibration Digest,13,4(1981),17-28. [4] Roberts,J.B.,Response of nonlinear mechanical systems to random excitation,Part 2:Equivalent linearization and other methods,The Shock and Vibration Digest,13,5(1981),15-29. [5] Roberts,J.B.,Techniques for non-linear random vibration problems,The Shock and Vibration Digest,16,9(1984),3-14. [6] Caughey,T.K.and F.Ma,The exact steady-state solution of a class of non-linear stochastic systems,Int.J.Non-Linear Mechanics,17(1982),137-142. [7] Caughey,T.K.and F.Ma,The steady-state response of a class of dynamical systems to stochastic excitation,J.Appl.Mech.,49(1982),629-632. [8] Dimentberg,M.F.,An exact solution to a certain non-linear random vibration problem,Int.J.Non-Linear Mechanics,17(1982),231-236. [9] Yong,Y.and Y.K.Lin,Exact stationary-response solution for second order nonlinear systems under parametric and external white-noise excitations,J.Appl.Mech.,54(1987),414-418. [10] Dimentberg,M.F.,Nonlinear Stochastic Problems of Mechanical Vibrations,Nauka,Moscow(1980).

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

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