Reflection of micropolar elastic waves at the non-free surface of a micropolar elastic half-space

Abstract

The reflection problem of the micropolar elastic waves at the non-free surface of a micropolar elastic half-space is studied in this paper. Different from the classic elastic solid, there are four kinds of elastic waves in the micropolar elastic solid and three of them are dispersive. The boundary conditions at the non-free surface of a micropolar elastic half-space are used to obtain the linear algebraic equation sets 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. At last, the influence of the boundary parameters, which reflect the mechanical behavior of the non-free surface, on the reflection energy partition of micropolar elastic waves is discussed based on the numerical results. Two cases of incident longitudinal displacement wave and incident coupled transverse displacement and transverse microrotational wave are considered.