Vol. 4, No. 10, 2009

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ISSN: 1559-3959
Moment Lyapunov exponents and stochastic stability for two coupled oscillators

Predrag Kozić, Goran Janevski and Ratko Pavlović

Vol. 4 (2009), No. 10, 1689–1701
Abstract

The Lyapunov exponent and moment Lyapunov exponent of two degree-of-freedom linear systems subjected to white noise parametric excitation are investigated. Through a perturbation method we obtain the explicit asymptotic expressions for these exponents in the presence of low intensity noise. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining the almost-sure and moment stability of a stochastic dynamical system. As an example, we study the almost-sure and moment stability of the flexural-torsion stability of a thin elastic beam subjected to a stochastically fluctuating follower force. The validity of the approximate results for moment Lyapunov exponents is checked by a numerical Monte Carlo simulation for these stochastic systems.

Keywords
elastic beam, eigenvalue, perturbation, stochastic stability, mechanics of solids and structures
Milestones
Received: 27 October 2008
Revised: 23 February 2009
Accepted: 19 June 2009
Published: 27 February 2010
Authors
Predrag Kozić
Department of Mechanical Engineering
University of Niš
Medvedeva 14
18000 Niš
Serbia
Goran Janevski
Department of Mechanical Engineering
University of Niš
Medvedeva 14
18000 Niš
Serbia
Ratko Pavlović
Department of Mechanical Engineering
University of Niš
Medvedeva 14
18000 Niš
Serbia