Transient stochastic response of quasi integerable Hamiltonian systems

被引：4

作者：

Liu, Zhong-Hua ^{[1
]}

Geng, Jian-Hua ^{[1
]}

Zhu, Wei-Qiu ^{[2
]}

机构：

[1] Xiamen Univ, Dept Civil Engn, Xiamen 361005, Peoples R China

[2] Zhejiang Univ, Dept Mech, State Key Lab Fluid Power Transmiss & Control, Hangzhou 310027, Zhejiang, Peoples R China

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; NONSTATIONARY PROBABILITY DENSITIES; APPROXIMATE METHOD;

D O I：

10.1007/s10409-013-0044-z

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The approximate transient response of quasi integrable Hamiltonian systems under Gaussian white noise excitations is investigated. First, the averaged It 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.

引用

页码：602 / 611

页数：10

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