Generalized thermoelasticity of a piezoelectric layer

Abstract

In the present research, the response of a one-dimensional piezoelectric layer is investigated using the generalized thermoelasticity theory of Lord and Shulman. The layer is subjected to thermal shock on one surface. Three coupled equations, namely, motion equation, energy equation and Maxwell equation in terms of displacement, temperature, and electric potential are established. Using the proper transformation, the mentioned equations are given in a dimensionless form. These equations are discretized by means of the generalized differential quadrature method and traced in time by means of the Newmark time marching scheme. Numerical examples are provided to show the propagation and reflection of thermal, mechanical and electrical waves in a layer. It is shown that under the Lord and Shulman theory, temperature propagates with a finite speed, similar to mechanical displacement wave. However, the electric displacement and potential propagate with infinite speed.

Keywords:

• Generalized differential quadrature
• Lord–Shulman theory
• Maxwell equation
• Newmark time marching method
• piezoelectric layer