Nonlinear dynamic response of acoustically excited and thermally loaded composite plates resting on elastic foundations

In order to ensure integrity of thermal protection system (TPS) subjected to a combination of thermal and acoustic loadings, a thin composite plate resting on a two-parameter elastic foundation is used to characterize the behavior of the thin top facesheet of TPS. The nonlinear dynamic response of a thermal loaded, acoustic excited plate is investigated. A theoretical model is developed based on Kirchhoff thin plate assumptions and von Kármán-type equation. General static condensation and Galerkin's method are used to derive a set of ordinary differential equations with cubic nonlinearity related to nonlinear coupling between mid-plane stretching and transverse deflection. The reduced-order model has been validated by comparison of postbuckled displacements with those obtained from full-order FEM analysis. Variations of transverse displacement and in-plane strain statistics with acoustic loading level and temperature rising are presented. It is proposed that the in-plane strain located on the plate surface is dominated by the competition of the linear and quadratic nonlinear modal amplitude terms, thus the characteristic of the strain histogram can be used to identify oscillation transition from no snap-through to persistent dynamic snap-through for the thermally buckled plate. The skewness of the strain histogram can be used to evaluate the degree of dynamic geometrical nonlinearity quantitatively for the postbuckled plate with symmetric snap-through motion.