Analysis of harmonic plane wave propagation predicted by strain and temperature-rate-dependent thermoelastic model

Abstract

ABSTRACT The present work is concerned with a novel generalized thermoelasticity theory introduced by Yu et al. [A modified Green-Lindsay thermoelasticity with strain rate to eliminate the discontinuity. Meccanica. 2018;53:2543–2554] which considers the strain-rate along with temperature-rate term in the constitutive equations. This theory is an attempt to modify the Green-Lindsay (GL) thermoelasticity theory. For an unbounded isotropic homogeneous elastic medium, the present work analyzes the propagation of plane harmonic waves in the context of this new theory. In order to investigate the effects of strain-rate term, the unified governing equations related to three thermoelastic models namely, classical coupled thermoelastic model, GL model and new model have been considered. The dispersion relation for the propagation of longitudinal plane waves in the contexts of all three models has been derived in a unified way, which is further solved by the computational tool for a particular material. The behavior of different wave components for longitudinal waves is examined through graphical representation and the effects of temperature-rate and strain-rate terms on the plane wave propagation are investigated. Significant differences in predictions by this new model as compared to other models are highlighted.