Control of the transient thermoelastic displacement of a functionally graded rectangular plate bonded to a piezoelectric plate due to nonuniform heating

Abstract

In this study, the theoretical analysis of a control of the transient thermoelastic displacement is developed for a functionally graded rectangular plate bonded to a piezoelectric plate due to nonuniform heat supply. Assuming that the functionally graded plate has nonhomogeneous thermal and mechanical material properties in the thickness direction, the three-dimensional temperature in a transient state and the three-dimensional transient thermal stresses of a simply supported plate for a functionally graded material are analyzed by introducing the theory of laminated composites as a theoretical approximation. By using the solution for a functionally graded plate and the exact solution for a piezoelectric plate of crystal class mm2, the theoretical analysis of three-dimensional transient piezothermoelasticity is developed for a simply supported combined plate. the analysis of a piezothermoelastic problem leads to an appropriate electric potential applied to the piezoelectric plate which suppresses the induced thermoelastic displacement in the thickness direction at the midpoint on the free surface of the functionally graded plate. As an example, numerical calculations are carried out for a functionally graded rectangular plate made of zirconium oxide and titanium alloy, bonded to a piezoelectric plate of a cadmium selenide solid. Some numerical results when the transient thermoelastic displacements are controlled are shown in figures.