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.
Stochastic Stability of Coupled Oscillators in Resonance: A Perturbation Approach
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, January 30, 2002; final revision, March 18, 2004. Associate Editor: A. A. Ferri. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California—Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
- Views Icon Views
- Share Icon Share
- Search Site
Namachchivaya, N. S., and Van Roessel, H. J. (January 27, 2005). "Stochastic Stability of Coupled Oscillators in Resonance: A Perturbation Approach ." ASME. J. Appl. Mech. November 2004; 71(6): 759–768. https://doi.org/10.1115/1.1795813
Download citation file: