Lyapunov Exponents and Stochastic Stability of Coupled Linear Systems Under Real Noise Excitation

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

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

J. Appl. Mech 59(3), 664-673 (Sep 01, 1992) (10 pages) doi:10.1115/1.2893775 History: Received October 03, 1990; Revised April 29, 1991; Online March 31, 2008


The almost-sure asymptotic stability of a class of coupled multi-degrees-of-freedom systems subjected to parametric excitation by an ergodic stochastic process of small intensity is studied. Explicit asymptotic expressions for the largest Lyapunov exponent for various values of the system parameters are obtained by using a combination of the method of stochastic averaging and a well-known procedure due to Khas’minskii, from which the asymptotic stability boundaries are determined. As an application, the example of the flexural-torsional instability of a thin elastic beam acted upon by a stochastically fluctuating load at the central cross-section of the beam is investigated.

Copyright © 1992 by The American Society of Mechanical Engineers
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