Generalized piezothermoelasticity of hollow spheres under thermal shock using Lord–Shulman theory

Abstract

Present investigation deals with the response of a piezoelectric hollow sphere that is subjected to sudden thermal shock. Loading and boundary conditions are assumed to be symmetric so the response of the sphere is also considered to be symmetric. The governing equations of the vessel are obtained which are three in number. These equations include the equation of motion, the energy equation and the Maxwell equation. The energy equation is established in the framework of single relaxation time theory of Lord and Shulman. The established equations are written in terms of temperature change, radial displacement, and electric potential. These equations are provided in a dimensionless presentation for the sake of generality. After that with the aid of the generalized differential quadrature method, the established equations are discreted. Also Newmark time marching scheme is applied to trace the radial displacement, electric potential, and temperature change in time domain. Novel numerical results are then provided to explore the propagation and reflection of electrical, thermal and mechanical waves in a hollow sphere. It is shown that temperature wave propagates with finite speed within the framework of the Lord–Shulman theory.