Time harmonic waves in a thermo-viscoelastic material with voids

Abstract

In the present work, we study the propagation of time harmonic waves in an infinite thermo-viscoelastic material with voids. Four basic waves traveling with distinct speeds are found, out of which, one is a shear wave, and the remaining three are dilatational waves. All the dilatational waves are found to be coupled due to the presence of voids and thermal properties of the material, while the shear wave is found to be uncoupled and travels independently with the speed that exists in a linear viscoelastic medium. The speeds of propagation of all the waves are found to be complex valued and frequency dependent. Reflection phenomena of these waves from a mechanically stress-free and thermally insulated plane boundary of a thermo-viscoelastic half-space with voids have been investigated. Formulae for amplitudes and energy ratios corresponding to various reflected waves have been obtained and are presented in closed form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.