Analytical solution for thermoelastic response of a thin plate subjected to temperature shock

This paper presents an analytical solution for the dynamic deflection field of a homogeneous thin plate under a temperature shock. The solution is derived by solving a one-dimensional heat conduction problem with mixed initial-boundary conditions (incorporating second and third kind boundary conditions), followed by the corresponding thermoelasticity problem. Fourier's law governs the heat transfer analysis. The thermoelastic response is formulated using the Sophie Germain equation, augmented by an inertial term. The plate exhibits constant thermophysical properties, with one edge rigidly clamped and the remaining three edges free. The objectives are to obtain an analytical solution and analyze its utility for practical applications. This solution will provide practical advantages - for example, in developing laws for controlling the angular motion of a small spacecraft taking into account the temperature shock of solar panels. The results are applicable to characterizing dynamic disturbances induced by temperature shock in spacecraft solar array panels.