Nonlinear random response of panels in an elevated thermal-acoustic environment

Sonic fatigue is generally considered as being one of the major design areas for the newest generation of high-speed flight vehicles. Efficient analysis methods for predicting nonlinear random response and fatigue life are urgently needed. This paper presents a finite element formulation for the prediction of nonlinear random response of thin isotropic/composite panels subjected simultaneously to high acoustic loads and elevated temperatures. Laminated plate theory and von Karman large displacement relations are used to derive the nonlinear equations of motion for an arbitrarily laminated composite panel subjected to combined acoustic and thermal loads. The nonlinear equations of motion in physical degrees of freedom are transformed to a set of coupled nonlinear equations in truncated modal coordinates, retaining fewer degrees of freedom. Numerical integration is employed to obtain the panel response to simulated Gaussian band-limited white noise. To validate the formulation, results are compared with existing linear and nonlinear solutions to assess the accuracy of nonlinear modal stiffness matrices and simulated random loads. Examples are given for an isotropic panel at various combinations of sound pressure levels and temperatures. Numerical results include rms values of maximum deflection and strain, time histories of deflection and strain response, probability distribution functions, power spectrum densities, and higher statistical moments. Numerical results predicted all three types of panel motions for a thermal buckled simply supported isotropic plate: linear random vibration about one of the buckled equilibrium position, snap-through motions between the two buckled positions, and nonlinear random response over both buckled positions.