Study of Two-Temperature Generalized Thermo-Piezoelastic Problem

Abstract

This article deals with the thermoelastic interaction in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading. In the context of two-temperature generalized thermoelasticity theory (IMA-2006) the three-phase-lag (3P) thermoelastic model [1], Green-Naghdi model III (GNIII) and Lord-Shulman model (LS) are employed to study the thermophysical quantities. The theory of 3P lag heat conduction equation leads to a fourth order partial differential equation. The basic equations have been written in the form of vector-matrix differential equation in Laplace-transform domain which is then solved by state-space approach. The numerical inversion of the transform is carried out by a method based on Fourier-series expansion techniques. The numerical estimates of the conductive temperature, the strain and the stress distributions are obtained and are shown graphically. The effect of two-temperature and electric field on the solutions have been studied and the comparison of results among different thermoelastic models are made.

Keywords:

• Generalized thermopiezo-elasticity
• GN model III
• LS model
• Three-phase-lag thermoelastic model
• Vector-matrix differential equation

ACKNOWLEDGEMENT

We are grateful to Prof. S. C. Bose of the Department of Applied Mathematics, University of Calcutta for his valuable suggestions and guidance in preparation of the article.