A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity

Abstract

a b s t r a c tThe aim of the present paper is to study the thermoelastic interactions in an unbounded elastic medium with a spherical cavity in the context of four different theories of thermoelasticity, namely: the classical coupled dynamical thermoelasticity, the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation in a unified way. The cavity surface is assumed to be stress free and is subjected to a smooth and time-dependent-heating effect. The solutions for displacement, temperature and stresses are obtained with the help of the Laplace transform procedure. Firstly the short-time approximated solutions for four different theories have been obtained analytically. Then following the numerical method proposed by Bellman et al. [R. Bellmen, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Pub. Co., New York, 1966] for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained for the theory of thermoelasticity without energy dissipation with the results of other thermoelasticity theories.

State-space approach to thermoelastic interactions in generalized thermoelasticity type III

“…(21) to (25) into the Eq. (15) and using (17) we finally get the solutions for the distributions of displacement, temperature and stress in the Laplace transform domain as follows:…”

“…Chandrasekhariah and Srinath [4,5] have studied cylindrical/spherical wave due to (1) a load applied to the boundary of cylindrical/spherical cavity in an unbounded body and (2) a line/point heat source in an unbounded body. Mukhopadhyay [16] and Mukhopadhyay and Kumar [17] analyzed one-dimensional problem in a half space without energy dissipation by state-space approach and the thermoelastic interactions without energy dissipation in an unbounded medium with a spherical cavity respectively. Taheri et al [19] considered an annulus and using GN-III model discussed the wave propagation and reflection from boundary and the influence of damping parameter on temperature, displacement and stress under different types of boundary conditions.…”

On Discontinuties in Thermoelastic Plane Waves without Energy Dissipation Due to a Thermo-Mechanical Shock

“…The uniqueness of solution for TEOWED theory has been studied by Chandrasekharaiah (1996a;1996b). Several investigations relating to TEWOED were presented by Roychoudhuri and Datta (2005), Sharma and Chouhan (1999), Roychoudhury and Bandyapadhyay (2004;2005), Mukhopadhyay (2002;2004) and Mukhopadhyay and Kumar (2008).…”

A generalized thermoelastic dual-phase-lagging response of thick beams subjected to harmonically varying heat and pressure

“…Ram et al (2008) obtained a general solution to the field equations of a harmonically timedependent generalized thermodiffusion in an elastic solid. Mukhopadhyay and Kumar (2008) studied thermoelastic interactions in a spherical-cavity medium subjected to a time-dependentheating effect in the context of different thermoelasticity theories. Gue et al (2012) analyzed thermoelastic damping of a micro-beam resonator by the dual-phase-lag thermal conduction model of the generalized thermoelasticity theory.…”