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RESEARCH PAPERS

Lyapunov Exponents and Stochastic Stability of Two-Dimensional Parametrically Excited Random Systems

[+] Author and Article Information
S. T. Ariaratnam, Wei-Chau Xie

Solid Mechanics Division, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

J. Appl. Mech 60(3), 677-682 (Sep 01, 1993) (6 pages) doi:10.1115/1.2900857 History: Received May 03, 1991; Revised March 30, 1992; Online March 31, 2008

Abstract

The variation of the largest Lyapunov exponent for two-dimensional parametrically excited stochastic systems is studied by a method of linear transformation. The sensitivity to random disturbance of systems undergoing bifurcation is investigated. Two commonly occurring examples in structural dynamics are considered, where the random fluctuation appears in the stiffness term or the damping term. The boundaries of almost-sure stochastic stability are determined by the vanishing of the largest Lyapunov exponent of the linearized system. The validity of the approximate results is checked by numerical simulation.

Copyright © 1993 by The American Society of Mechanical Engineers
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