Dynamic problem in 3D thermoelastic half-space with rotation in context of G-N type II and type III

S Santra,N C Das,A Lahiri

doi:10.21595/mme.2017.18143

Abstract

In this paper, comparison between G-N model of type II (without energy dissipation) and G-N model of type III (with energy dissipation) has been shown in a three dimensional thermoelastic half space with rotation subjected to time dependent heat source on the traction free boundary. Eigenvalue methodology has been adopted to solve the equations resulting from the application of the Normal mode analysis to the non-dimensional coupled equations. Variation of the numerically computed values of thermal stresses and temperature with and without rotation has been illustrated graphically.

Highlights

The inconsistency of heat conduction equation of classical uncoupled theory of thermoelasticity with the experimental results is due to the fact that i. no elastic term is included to account for elastic changes producing heat effects; ii. parabolic nature of heat conduction equation indicating infinite speed of propagation of heat waves means that thermal disturbances and elastic disturbances from the classical theory of thermoelasticity, are coupled together
Biot [1] developed a theory of irreversible thermodynamics and gave a satisfactory derivation of the linear theory of coupled thermoelasticity
In order to obtain a wave type heat conduction equation the concept of generalized thermoelasticity was introduced modifying CCTE and later extended by Dhaliwal and Sherief [3] for anisotropic body, and the uniqueness of the solutions was proved by Ignaczak [2, 4]

Summary

Introduction

The inconsistency of heat conduction equation of classical uncoupled theory of thermoelasticity with the experimental results is due to the fact that i. no elastic term is included to account for elastic changes producing heat effects; ii. parabolic nature of heat conduction equation indicating infinite speed of propagation of heat waves means that thermal disturbances (with infinite speed) and elastic disturbances (with finite speed) from the classical theory of thermoelasticity, are coupled together. Parabolic nature of heat conduction equation indicating infinite speed of propagation of heat waves means that thermal disturbances (with infinite speed) and elastic disturbances (with finite speed) from the classical theory of thermoelasticity, are coupled together. This suggests that every solution of the equations has a part which extends to infinity. Type-II provides solutions for thermal waves propagating finite speed without energy dissipation (TEWOED) and type-III confirms propagation of thermal waves of finite speed with energy dissipation (TEWED) Several investigations with these extensions have been studied by Abd-Alla and Abo-Dahab [11], Kar and Kanoria [9] and Yousef [10]. The stress distributions and temperature variation has been depicted in an anisotropic triclinic half space for G-N model II and III both with rotation

Basic equations

Formulation of the problem

Normal mode analysis

Solution of the vector- matrix differential equation: eigenvalue approach

Boundary conditions

Conclusions