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


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
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In