Stochastic Dynamics of a Nonlinear Aeroelastic System

摘要

We investigate the asymptotic behaviors of a thin panel in high supersonic flow with a turbulent boundary layer. The objective of this investigation is achieved by formulating methods to analyze complex interactions among aerodynamic/structural dynamic nonlinearities, turbulence, and stability. We reduce an infinite dimensional model to a finite dimensional system in the Galerkin's sense. The normal form technique is employed not only to capture the essential dynamics of the system in which significant nonlinearities are considered but also to reduce the dimensionality of the dynamical system. Because of the random nature of forcing characteristics associated with the turbulence, the theory of stochastic processes is used to explore panel responses in the presence of turbulent boundary layer. After adequate scaling of parameters, a nonstandard reduction through stochastic averaging is achieved. It turns out that the solution of the reduced model is approximated by a Markov process that takes its value on a graph with gluing conditions that furnish the complete specification of the dynamics of the reduced model. With the aid of the infinitesimal generator of the reduced Markov process on the graph, we examine stochastic analyses such as mean exit time, probability density and stochastic bifurcation in the phenomenological sense.