Equivalent Nonlinear System Method for Stochastically Excited Hamiltonian Systems

[+] Author and Article Information
W. Q. Zhu, T. T. Soong

Department of Civil Engineering, State University of New York, Buffalo, NY 14260

Y. Lei

Department of Architectural Engineering, Shantou University, Shantou, Guangdong, China

J. Appl. Mech 61(3), 618-623 (Sep 01, 1994) (6 pages) doi:10.1115/1.2901504 History: Received September 04, 1992; Revised May 12, 1993; Online March 31, 2008


An equivalent nonlinear system method is presented to obtain the approximate probability density for the stationary response of multi-degree-of-freedom nonlinear Hamiltonian systems to Gaussian white noise parametric and/or external excitations. The equivalent nonlinear systems are obtained on the basis of one of the following three criteria: least mean-squared deficiency of damping forces, dissipation energy balancing, and least mean-squared deficiency of dissipation energies. An example is given to illustrate the application and validity of the method and the differences in the three equivalence criteria.

Copyright © 1994 by The American Society of Mechanical Engineers
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