Moment Lyapunov exponent and stochastic stability for a binary airfoil driven by an ergodic real noise. (English) Zbl 1281.76023
Summary: This paper presents a new method, through which the \(p\)th moment stability of a binary airfoil subjected to an ergodic real noise is obtained. The excitation included is assumed to be an integrable function of an \(n\)-dimensional Ornatein-Uhlenbeck vector process that is the output of a linear filter system and for which the strong mixing condition and the delicate balance condition are removed in the present study. By using a perturbation method and the spectrum representations of both the Fokker-Planck operator and its adjoint operator of the linear filter system, the asymptotic expressions of the \(p\)th moment Lyapunov exponent are obtained, and the results of which match the numerical results.
MSC:
| 76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
| 35Q84 | Fokker-Planck equations |
| 93E15 | Stochastic stability in control theory |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
Keywords:
moment stability; stochastic processes; Fokker-Planck equation; binary airfoil; ergodic real noiseReferences:
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