Transient stochastic response of quasi integerable Hamiltonian systems

被引：0
作者：
Zhong-Hua Liu
Jian-Hua Geng
Wei-Qiu Zhu
机构：
[1] Xiamen University,Department of Civil Engineering
[2] Zhejiang University,Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control
来源：
Acta Mechanica Sinica | 2013年 / 29卷
关键词：
Transient response; Stochastic averaging method; Galerkin method; Quasi integrable Hamiltonian system;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The approximate transient response of quasi integrable Hamiltonian systems under Gaussian white noise excitations is investigated. First, the averaged Itô equations for independent motion integrals and the associated Fokker-Planck-Kolmogorov (FPK) equation governing the transient probability density of independentmotion 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.
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页码：602 / 611
页数：9
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