Reflection of elastic waves at the elastically supported boundary of a couple stress elastic half-space

Abstract

The reflection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of reflection waves to the incident wave can be determined. Then, the reflection coefficients in terms of energy flux ratios are calculated numerically, and the normal energy flux conservation is used to validate the numerical results. Based on these numerical results, the influences of the boundary parameters, which reflect the mechanical behavior of elastic support, on the reflection energy partition are discussed. Both the incident longitudinal wave (the P wave) and incident transverse wave (the SV wave) are considered.