On the moment lyapunov exponent of a viscoelastic plate subjected to the excitation of wide band noises

In the present paper, the moment Lyapunov exponent of aviscoelastic plate in a supersonic gas flow subjected to the excitation ofwide band noises is investigated. A aeroelastic model for two coupleddegrees-of-freedom panel is established by using the Von Karman platestheory, the quasi-first-order piston theory and Galerkin approximation. Viathe stochastic averaging method, the four-dimensional system is reduced to atwo-dimensional one. Through the logarithmic polar transformation , and thenGirsanov theorem and Feynmann-Kac formula, the backward differentialoperator is then obtained. By expanding the eigenfunctions as a Fouriercosine series, the approximate analytic expansion of the moment Lyapunovexponent is then obtained and matched by the Monte Carle simulation results.Finally, the influences of the system parameters, gas dynamical parametersand the spectral density of noises on the stochastic stability ofviscoelastic plate is studied.