Transient stochastic response of quasi integerable Hamiltonian systems  

作　　者：Zhong-Hua Liu Jian-Hua Geng Wei-Qiu Zhu 

机构地区：[1]Department of Civil Engineering, Xiamen University [2]Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University

出　　处：《Acta Mechanica Sinica》2013年第4期602-611,共10页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(10902094,10932009,11072212 and 11272279);the Special Foundation for Young Scientists of Fujian Province of China(2008F3100)

摘　　要：The approximate transient response of quasi in- tegrable Hamiltonian systems under Gaussian white noise excitations is investigated. First, the averaged It6 equa- tions 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 averag- ing 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 approxi- mate transient solution is expressed as a series in terms of properly selected base functions with time-dependent coeffi- cients. The transient probability densities of displacements and velocities can be derived from that of independent mo- tion integrals. Three examples are given to illustrate the ap- plication of the proposed procedure. It is shown that the re- suits for the three examples obtained by using the proposed procedure agree well with those from Monte Carlo simula- tion of the original systems.The approximate transient response of quasi in- tegrable Hamiltonian systems under Gaussian white noise excitations is investigated. First, the averaged It6 equa- tions 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 averag- ing 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 approxi- mate transient solution is expressed as a series in terms of properly selected base functions with time-dependent coeffi- cients. The transient probability densities of displacements and velocities can be derived from that of independent mo- tion integrals. Three examples are given to illustrate the ap- plication of the proposed procedure. It is shown that the re- suits for the three examples obtained by using the proposed procedure agree well with those from Monte Carlo simula- tion of the original systems.

关 键 词：Transient response ~ Stochastic averagingmethod ~ Galerkin method ~ Quasi integrable Hamiltoniansystem 

分 类 号：O241.83[理学—计算数学]