Stochastic Averaging of Quasi-Nonintegrable-Hamiltonian Systems

[+] Author and Article Information
W. Q. Zhu, Y. Q. Yang

Department of Mechanics, Zhejiang University, Hangzhou, 310027, P. R. China

J. Appl. Mech 64(1), 157-164 (Mar 01, 1997) (8 pages) doi:10.1115/1.2787267 History: Received December 01, 1994; Revised September 17, 1996; Online October 25, 2007


A stochastic averaging method is proposed to predict approximately the response of multi-degree-of-freedom quasi-nonintegrable-Hamiltonian systems (nonintegrable Hamiltonian systems with lightly linear and (or) nonlinear dampings and subject to weakly external and (or) parametric excitations of Gaussian white noises). According to the present method, a one-dimensional approximate Fokker-Planck-Kolmogorov equation for the transition probability density of the Hamiltonian can be constructed and the probability density and statistics of the stationary response of the system can be readily obtained. The method is compared with the equivalent nonlinear system method for stochastically excited and dissipated nonintegrable Hamiltonian systems and extended to a more general class of systems. An example is given to illustrate the application and validity of the present method and the consistency of the present method and the equivalent nonlinear system method.

Copyright © 1997 by The American Society of Mechanical Engineers
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