Coupled and uncoupled thermally induced vibration of FGM plate

The present study investigates the coupled and uncoupled dynamic thermoelastic response of a thin functionally graded material (FGM) plate subjected to transient thermal shock loading. The plate is graded in the thickness direction, with the top surface exposed to a sudden heat flux and the bottom surface thermally insulated. The governing equations are derived using Hamilton’s principle based on first-order shear deformation theory, assuming small linear strains and incorporating the heat conduction equation. These equations are discretized using the generalized differential quadrature (GDQ) method and solved by the Newmark time integration scheme to obtain transient temperature and displacement fields. Due to the thinness of the plate, a linear temperature profile through the thickness is assumed. The study specifically focuses on the transient behavior of the structure and considers the role of thermoelastic coupling in energy dissipation during vibrations, as predicted by the coupled thermoelasticity theory. The results are validated against existing solutions, and a comprehensive parametric study is conducted to examine the influence of material gradient index, plate geometry, boundary conditions, and thermal loading characteristics on the dynamic responses.