Generalized thermo-electro-elasticity of a piezoelectric disk using Lord-Shulman theory

Abstract

Current investigation deals with the generalized thermoelastic response of a finite hollow disk made of a piezoelectric material. The constitutive equations of the piezoelectric media are reduced to a two dimensional plane-stress state. To capture the finite speed of temperature wave, the single relaxation time theory of Lord and Shulman is used. Three coupled differential equations in terms of radial displacement, electric potential, and temperature change are obtained. These equations are written in a dimensionless presentation. With the aid of the differential quadrature method (DQM) a time-dependent algebraic system of equations is extracted. The Newmark time marching scheme is applied to trace the temporal evolution of temperature change, electric potential, radial displacement, stresses, and electric displacement. Numerical results demonstrate that radial displacement and temperature waves propagate with finite speed while the electric potential propagates with infinite speed.