Nonlinear Random Response Analyses of Panels Considering Transverse Shear Deformations under Combined Thermal and Acoustic Loads

Abstract

The panel structures of flight vehicles at supersonic or hypersonic speeds are subjected to combined thermal, acoustic, and aerodynamic loads. Because of the combined thermal and acoustic loads, the panel structure may exhibit nonlinear random vibration responses, such as the snap-through phenomenon and random vibrations. These unique dynamic behaviors of the panel structure under combined thermal and acoustic loads can result in serious damage or fatigue failure of the panel structures of high-speed flight vehicles. This study investigates the nonlinear random responses of thin and thick panels under combined thermal and acoustic loads. The panels are modeled based on the first-order shear deformation theory (FSDT) to account for transverse shear deformations. The von-Karman nonlinear strain–displacement relationship is used for geometric nonlinearity in the out-of-plane direction of the panel. The thermal load distribution is assumed to be constant in the thickness direction of the panel. The random acoustic load is represented as stationary White–Gaussian random pressure with zero mean and uniform magnitude over the panels. Static and dynamic equations are derived using the principle of virtual work and the nonlinear finite element method. A thermal postbuckling analysis is conducted using the Newton–Raphson method, and the dynamic nonlinear equations are solved using the Newmark-β time integration method. In the present numerical analyses, the snap-through responses for both the thin and thick panels are investigated, and the results indicate that the loading conditions that cause snap-through are different for thin and thick panels.