Propagation of Plane Waves in Generalized Piezo-thermoelastic Medium: Comparison Of Different Theories

ABSTRACT: In this paper, a general solution for the propagation of plane waves in generalized piezo-thermoelastic medium for two-dimensional problem under the different thermoelastic theories is investigated. We have included Coupled theory (CT), Lord-Schulman (L-S) and Green-Lindsay (G-L) theories. The normal mode analysis is used to obtain the exact expressions for the considered variables. The results of the physical quantities have been illustrated graphically by comparison between (CT), (L-S) and (G-L) theories. KEYWORDS: Piezo-thermoelastic, Relaxation time, Normal mode analysis, Generalized thermoelasticity. I INTRODUCTION Piezoelectric is considered one of the basic properties of crystals, ceramics, polymers, liquid crystals and some biological tissues (e.g. bone and tendon). Recent interest in the piezoelectric materials stems from their potential applications in intelligent structural systems, and piezoelectric is currently enjoying a greatest resurgence in both fundamental research and technical applications. The theory of thermo-piezoelectric was first proposed by Mindlin Thermoelasticity theories that predict a finite speed for the propagation of thermal signals have aroused much interest in the last three decades. These theories are known as generalized thermoelasticity theories. The first generalization of the thermoelasticity theory is due to Lord and Shulman [8] who introduced the theory of generalized thermoelasticity with one relaxation time through postulating a new law of heat conduction to replace the classical Fourier' law. This law contains the heat flux vector as well as its time derivative. It contains also a new constant that acts as a relaxation time. The heat equation of this theory is of the wave-type which ensuring finite speeds of propagation of heat and elastic waves. The remaining, governing equations for this theory, namely, the equations of motion and the constitutive relations remain the same as those for the coupled and the uncoupled theories. This theory was extended by Dhaliwal and Sherief [9] to general anisotropic media in the presence of heat sources. Othman [10] studied the Lord