On propagation of harmonic plane waves under the Moore–Gibson–Thompson thermoelasticity theory

Abstract

ABSTRACT The present work is aimed at a detailed investigation of harmonic plane wave propagation through an isotropic, unbounded and homogeneous thermoelastic medium under the recently proposed Moore–Gibson–Thompson (MGT) thermoelasticity theory. The dispersion relation is derived and its solution for the longitudinal plane wave propagation is obtained analytically. Two different modes of longitudinal wave are identified as elastic and thermal mode waves. The asymptotic expressions of various important characteristics of the wave fields such as phase velocity, specific loss and penetration depth for both the waves are obtained for limiting cases of very high and low frequency values. The Whitham stability of harmonic plane waves is established. Further, the computational tool is used to achieve numerical results for these wave characteristics and to illustrate the analytical findings graphically. Some important observations about the prediction of the MGT model in comparison to the other existing models, i.e. classical coupled thermoelastic model, LS model and GN-III model, are highlighted. Effects of material parameters on the propagation of waves are analyzed in a detailed manner. From the theoretical as well as numerical results, it is investigated that the MGT model accounts for finite speed of elastic wave as well as thermal wave.