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.

Issue Section:
Technical Papers
Keywords:
nonlinear dynamical systems, stochastic processes, Galerkin method, stochastic systems, mechanical stability, eigenvalues and eigenfunctions, Lyapunov methods
Topics:
Eigenvalues, Resonance, Stability, Galerkin method, Generators, Noise (Sound), Excitation, Approximation
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