Reflection and Transmission of Thermoelastic Waves Through a Sandwiched Slab with Couple Stress

Abstract

The reflection and transmission of the thermos-elastic coupled waves across a slab of finite thickness that is sandwiched between two semi-infinite homogeneous isotropic couple stress elastic solids are studied. Based on the modified couple-stress theory and the Green-Lindsay theory, the governing equations of the thermoeleastic wave propagation are derived. Different from the classic elastic solid, the interface conditions involve the micro-rotation and the surface couple. The nontraditional interface conditions between the slab and two half-spaces are used to obtain the linear algebraic equations set from which the amplitude ratios of reflection and transmission waves can be determined. Then, the energy fluxes carried by reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. At last, the influences of two thermal relaxation times are discussed based on the numerical results. It is found that the thermos-elastic coupling makes the longitudinal wave and the thermal wave not only dispersive but also attenuated, and the thermal wave effect mainly affects the dilatational waves.