Equivalent Nonlinear System Method for Stochastically Excited and Dissipated Integrable Hamiltonian Systems

[+] Author and Article Information
W. Q. Zhu

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

Y. Lei

Department of Architectural Engineering, Shantou University, Shantou 515063, Guangdong, P. R. China

J. Appl. Mech 64(1), 209-216 (Mar 01, 1997) (8 pages) doi:10.1115/1.2787275 History: Received October 04, 1995; Revised July 19, 1996; Online October 25, 2007


An equivalent nonlinear system method is proposed to obtain the approximate probability density for the stationary response of multi-degree-of-freedom integrable Hamiltonian systems with linear and (or) nonlinear dampings and subject to external and (or) parametric excitations of Gaussian white noises. The equivalent nonlinear systems are obtained on the basis of one of the following three criteria: least mean-squared difference in damping forces, dissipation energy balancing, or least mean-squared difference in dissipation energies. Two examples are given to illustrate the application and validity of the method and the differences in the three equivalence criteria. The method is also extended to a more general class of systems which include the stochastically excited and dissipated integrable Hamiltonian systems as special cases.

Copyright © 1997 by The American Society of Mechanical Engineers
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