Thermoacoustic response of a simply supported isotropic rectangular plate in graded thermal environments

A theoretical model is developed to investigate the thermoacoustic response of a simply supported plate subjected to combined thermal and acoustic excitations, with two typical graded thermal environments considered. The thermoacoustic governing equation derived by incorporating the thermal moments, membrane forces and acoustic loads into the plate vibration equation is solved using the modal decomposition approach. In combination with the thermal boundary conditions, the Fourier heat conduction equation is solved for the graded temperature distribution in the plate. Fluid-structure coupling between acoustic excitation and the plate is ensured by adopting the velocity continuity condition at the fluid-plate interface. With focus placed on the effect of graded thermal environments on plate vibroacoustic response, numerical investigations reveal the necessity for considering thermal moments in theoretical modeling, particularly when graded thermal environments are of common concern for aircraft structures.