Investigation on Transient Viscothermoelastic Waves in a Half-Space due to Instantaneous Thermal Point Heat Sources via Moore-Gibson-Thompson Heat Conduction Model

Abstract

The study in this paper deals with the investigation of the Moore-Gibson-Thompson model of generalized thermoelastic solid subjected to internal heat generation along the z-axis having axisymmetric heat supply. Governing equations of the problem have been derived for different models of thermoelasticity such as the Green-Naghdi III, Moore-Gibson-Thompson, and Lord-Shulman models. Time harmonics and Hankel transformation techniques are used to obtain solutions from governing equations to ordinary differential equations. The inverse Hankel transform is estimated by using numerical methods with the help of Romberg integration (Simpson’s one-third rule), followed by extrapolation to the limit as the step size tends to zero. Unknown field functions have been calculated from a system of equations obtained through boundary conditions using the Gauss Elimination numerical technique. Analytical results of temperature variations, displacements and stresses are derived from significant expressions authenticated with existing literature. Numerical results are represented graphically with respect to the radial distance for different models of thermoelasticity.