Reflection and Transmission of Inhomogeneous Plane Waves in Thermoelastic Media

Abstract

We study the reflection and transmission coefficients of plane waves incident at an interface between two isotropic thermoelastic half spaces and compare them with those of the elastic case. The models include the classical-Biot (B) and extended Lord-Shulman (LS) theories, and predict reflected and transmitted fast-compressional (P), thermal (T) and shear (S) waves. The coefficients are formulated in terms of incidence and inhomogeneity angles, medium properties and potential functions. We consider different incident wave types and inhomogeneity angles to analyze the magnitude, phase and energy ratio of the plane waves, and perform a comparison with the isothermal (elastic) theory. The thermoelastic and elastic models predict different energy partitions between the P and S modes, satisfying the conservation of energy. The LS model exhibits higher T-wave thermal attenuation with increasing inhomogeneity angle at high frequencies, accordingly predicting more interference energy. The angle affects the energy partitions, particularly at the critical angle and near grazing incidence for an incident P wave, which satisfies the conservation of energy. Beyond the critical angle, the energy flux perpendicular to the interface of the isothermal model vanishes, while it is significant in the thermoelastic case. The T-wave magnitudes increase when the thermal conductivity (relaxation time) increases.