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
收藏
页码：602 / 611
页数：10
相关论文
共 50 条
  • [1] Transient stochastic response of quasi integerable Hamiltonian systems
    Zhong-Hua Liu
    Jian-Hua Geng
    Wei-Qiu Zhu
    [J]. Acta Mechanica Sinica, 2013, 29 (04) : 602 - 611
  • [2] Transient stochastic response of quasi integerable Hamiltonian systems
    Zhong-Hua Liu
    Jian-Hua Geng
    Wei-Qiu Zhu
    [J]. Acta Mechanica Sinica, 2013, 29 : 602 - 611
  • [3] Transient stochastic response of quasi non-integerable Hamiltonian system
    Liu, Z. H.
    Geng, J. H.
    Zhu, W. Q.
    [J]. PROBABILISTIC ENGINEERING MECHANICS, 2016, 43 : 148 - 155
  • [4] Transient stochastic response of quasi-partially integrable Hamiltonian systems
    Liu, Z. H.
    Geng, J. H.
    Zhu, W. Q.
    [J]. ARCHIVE OF APPLIED MECHANICS, 2014, 84 (01) : 123 - 131
  • [5] Transient stochastic response of quasi-partially integrable Hamiltonian systems
    Z. H. Liu
    J. H. Geng
    W. Q. Zhu
    [J]. Archive of Applied Mechanics, 2014, 84 : 123 - 131
  • [6] Stochastic averaging of quasi-Hamiltonian systems
    朱位秋
    [J]. Science China Mathematics, 1996, (01) : 97 - 107
  • [7] Stochastic averaging of quasi-Hamiltonian systems
    Zhu, WQ
    [J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 1996, 39 (01): : 97 - 107
  • [8] STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS
    Deng Maolin (Department of Biomedical Engineering
    [J]. Acta Mechanica Solida Sinica, 2003, (04) : 313 - 320
  • [9] Stochastic optimal control for the response of quasi non-integrable Hamiltonian systems
    Deng, ML
    Hong, MC
    Zhu, WQ
    [J]. ACTA MECHANICA SOLIDA SINICA, 2003, 16 (04) : 313 - 320
  • [10] TRANSIENT STOCHASTIC RESPONSE OF QUASI-INTEGRABLE HAMILTONION SYSTEMS WITH VISCOELASTICITY
    Liu, Z. H.
    Geng, J. H.
    Zhu, W. Q.
    [J]. INNOVATION & SUSTAINABILITY OF STRUCTURES, VOLS 1 AND 2, 2011, : 1416 - 1421
12345