Moment Lyapunov Exponent and Stochastic Stability of Two Coupled Oscillators Driven by Real Noise-Reference-Cited by-同舟云学术

Moment Lyapunov Exponent and Stochastic Stability of Two Coupled Oscillators Driven by Real Noise

Published:2001-02-26 Issue:6 Volume:68 Page:903-914
ISSN:0021-8936
Container-title:Journal of Applied Mechanics
language:en
Short-container-title:

Author:

Sri Namachchivaya N.¹,Van Roessel H. J.²

Affiliation:

1. Department of Aeronautical and Astronautical Engineering, University of Illinois, 103 S. Wright Street, Urbana, IL 61801-2935

2. Department of Mathematical Sciences, University of Alberta, Edmonton AB, Canada

Abstract

In a recent paper an asymptotic approximation for the moment Lyapunov exponent, gp, of two coupled oscillators driven by a small intensity real noise was obtained. The utility of that result is limited by the fact that it was obtained under the assumption that the moment p is small, a limitation which precludes, for example, the determination of the stability index. In this paper that limitation is removed and an asymptotic approximation valid for arbitrary p is obtained. The results are applied to study the moment stability of the stationary solutions of structural and mechanical systems subjected to stochastic excitation.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Link

http://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/68/6/903/5468743/903_1.pdf

Reference12 articles.

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2. Arnold, L. , 1984, “A Formula Connecting Sample and Moment Stability of Linear Stochastic Systems,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 44, No. 4, pp. 793–802.

3. Arnold, L., Kliemann, W., and Oeljeklaus, E., 1986, Lyapunov Exponents of Linear Stochastic Systems, Vol. 1186 (Lecture Notes in Mathematics), Springer-Verlag, New York, pp. 85–125.

4. Arnold, L., Oeljeklaus, E., and Pardoux, E., 1986, Almost Sure and Moment Stability for Linear Ito^ Equations, Vol. 1186 (Lecture Notes in Mathematics), Springer-Verlag, New York, pp. 129–159.

5. Namachchivaya, N. Sri, Van Roessel, H. J., and Doyle, M. M., 1996, “Moment Lyapunov Exponent for Two Coupled Oscillators Driven by Real Noise,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 56, pp. 1400–1423.

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