Stochastic Analysis of a Nonlinear Forced Panel in Subsonic Flow With Random Pressure Fluctuations

Abstract

The stochastic behavior of a two-dimensional nonlinear panel subjected to subsonic flow with random pressure fluctuations and an external forcing is studied in this paper. The total aerodynamic pressure is considered as the sum of two parts, one given by the random pressure fluctuations on the panel in the absence of any panel motion, and the other due to the panel motion itself. The random pressure fluctuations are idealized as a zero mean Brownian motion. Galerkin method is used to transform the governing partial differential equation to a series of ordinary differential equations. The closed moment equations are obtained by the Itô differential rule and Gauss truncation. The stability and complex responses of the moment equations are presented in theoretical and numerical analysis. Results show that a bifurcation of fixed points occurs and the bifurcation point is determined as functions of noise spectral density, dynamic pressure, and panel structure parameters; the chaotic response regions and periodic response regions appear alternately in parameter spaces, the periodic responses trajectories change rhythmically, and the route from periodic responses to chaos is via doubling-period bifurcation. The treatment suggested in this paper can also be extended for the other fluid-structure dynamic systems.