Stochastic Stability of Coupled Oscillators in Resonance: A Perturbation Approach-Reference-Cited by-同舟云学术

Stochastic Stability of Coupled Oscillators in Resonance: A Perturbation Approach

Published:2004-11-01 Issue:6 Volume:71 Page:759-768
ISSN:0021-8936
Container-title:Journal of Applied Mechanics
language:en
Short-container-title:

Author:

Namachchivaya N. Sri¹,Van Roessel H. J.²

Affiliation:

1. Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

2. Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Abstract

A perturbation approach is used to obtain an approximation for the moment Lyapunov exponent of two coupled oscillators with commensurable frequencies driven by a small intensity real noise with dissipation. The generator for the eigenvalue problem associated with the moment Lyapunov exponent is derived without any restriction on the size of pth moment. An orthogonal expansion for the eigenvalue problem based on the Galerkin method is used to derive the stability results in terms of spectral densities. These results can be applied to study the moment and almost-sure stability 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/71/6/759/5471566/759_1.pdf

Reference13 articles.

1. Namachchivaya, N. Sri, and Van Roessel, H. J., 1993, “Maximal Lyapunov Exponent and Rotation Numbers for Two Coupled Oscillators Driven by Real Noise,” J. Stat. Phys., 71(3/4), pp. 549–567.

2. 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.

3. Namachchivaya, N. Sri, and Van Roessel, H. J., 2001, “Moment Lyapunov Exponent and Stochastic Stability of Two Coupled Oscillators Driven by Real Noise,” ASME J. Appl. Mech., 68, pp. 1400–1412.

4. Molc˘anov, S. A. , 1978, “The Structure of Eigenfunctions of One-Dimensional Unordered Structures,” Math. USSR, Izv., 12(1), pp. 69–101.

5. Arnold, L. , 1984, “A Formula Connecting Sample and Moment Stability of Linear Stochastic Systems,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 44(4), pp. 793–802.

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