Abstract
An asymptotic expansion for the maximal Lyapunov exponent, the exponential growth rate of solutions to a linear stochastic system, and the moment Lyapunov exponent, the asymptotic growth rate of the moments of the response, have been obtained for systems driven by a small intensity real noise process. The systems under consideration are general four-dimensional dynamical systems with two critical modes. Almost-sure and moment stability conditions are obtained provided the natural frequencies of these critical modes are non-commensurable and the infinitesimal generator associated with the noise process has an isolated simple zero eigenvalue. In this paper, the results obtained are applied to a thin rectangular beam under the action of a stochastic follower force and a model of a vehicle traveling over a rough road. The stability regions predicted by the two different criteria are then compared.
Original language | English (US) |
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Pages (from-to) | 681-692 |
Number of pages | 12 |
Journal | International Journal of Non-Linear Mechanics |
Volume | 32 |
Issue number | 4 |
DOIs | |
State | Published - Jul 1997 |
Keywords
- Almost-sure stability
- Follower force
- Moment stability
- Vibration absorber
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics