Reflection and refraction of thermoelastic waves at an interface of two couple-stress solids based on Lord-Shulman thermoelastic theory

Abstract

• The coupled governing equations of thermoelastic couple stress solid are derived in detail. • The thermal wave effects and the couple-stress effects are both studied. • The mechanically and thermally imperfect interface conditions are considered. • The transmission mechanism of waves across an imperfect interface is explained by three channels of energy flux. • The influences of the thermal relaxation time are discussed. The reflection and refraction of thermoelastic waves at an imperfect interface of two semi-infinite homogeneous isotropic thermoelastic couple stress solids are studied in this paper. First, the coupled governing equations and the constitutive equations of thermoelastic couple-stress medium are derived based on Lord-Shulman generalized thermoelastic theory. In contrast to the classical thermoelastic solid, there exist four kinds of wave modes (two coupled longitudinal waves and two transversal waves) in the thermoelastic couple-stress solid. Second, the reflection and refraction of these coupled thermoelastic waves across a mechanically and thermally imperfect interface are considered. The interfacial conditions result in a set of algebraic equations from which the reflection and refraction amplitudes ratios can be obtained for both incident CP-wave and incident SV-wave. The numerical results are shown graphically and the influences of the thermal relaxation time and the imperfect interface parameters are discussed. The transmission mechanism of waves across an imperfect interface is explained by three kinds of channels of energy flux.