Transient stochastic response of quasi integerable Hamiltonian systems

被引：0

作者：

Zhong-Hua Liu ^{[1
]}

Jian-Hua Geng ^{[1
]}

Wei-Qiu Zhu ^{[2
]}

机构：

[1] Department of Civil Engineering, Xiamen University

[2] Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University

来源：

Acta Mechanica Sinica | 2013年 / 29卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Transient response Stochastic averaging method Galerkin method Quasi integrable Hamiltonian system;

D O I：

暂无

中图分类号：

O241.83 [积分方程的数值解法];

学科分类号：

070102 ;

摘要：

The approximate transient response of quasi integrable Hamiltonian systems under Gaussian white noise excitations is investigated. First, the averaged Ito equations for independent motion integrals and the associated Fokker-Planck-Kolmogorov (FPK) equation governing the transient probability density of independent motion integrals of the system are derived by applying the stochastic averaging method for quasi integrable Hamiltonian systems. Then, approximate solution of the transient probability density of independent motion integrals is obtained by applying the Galerkin method to solve the FPK equation. The approximate transient solution is expressed as a series in terms of properly selected base functions with time-dependent coefficients. The transient probability densities of displacements and velocities can be derived from that of independent motion integrals. Three examples are given to illustrate the application of the proposed procedure. It is shown that the results for the three examples obtained by using the proposed procedure agree well with those from Monte Carlo simulation of the original systems.

引用

页码：602 / 611

页数：10

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