Plane waves in an isotropic thermoelastic diffusive material using strain gradient theory

Abstract

The governing equations of motion for an isotropic strain-gradient thermoelastic material with diffusion are formulated in context of Lord and Shulman generalization of thermoelasticity and are further specialised for a two dimensional plane. Plane harmonic solution of the governing equations in two-dimension suggests the existence of five plane waves which include four coupled longitudinal waves and a shear vertical wave. A numerical example is considered to illustrate graphically the effect of frequency, measure constant of diffusion, measure constant of thermo-diffusion, thermal relaxation time, diffusive relaxation time and the coefficients of hyperstress tensor on the phase speed and attenuation coefficients of the plane waves.