Reflection of longitudinal displacement wave at the viscoelastically supported boundary of micropolar half-space

The reflection of elastic waves at the boundary of micropolar half-space with the viscoelastic support is studied in this paper. The spring-dashpot model is used to model the viscoelastic support. The boundary condition includes the force stress, couple stress, the displacements and the micro-rotation and the contribution from the spring and the dashpot on them. The amplitude ratios and phase shifts of reflection waves with respect to the incident wave are obtained from the visco-elastic boundary conditions. Further, the energy flux ratios of the reflection waves to the incident wave are estimated and the energy flux conservation with consideration of the energy dissipation of visco-elastic boundary is used to validate the numerical results. Based on the numerical results, the influences of spring and dashpot are studied respectively. It is found that the elastically supported boundary and the viscously supported boundary have evident different influences on the amplitude ratio and the phase shift. The causes resulting in these deviations are related with the instantaneous elasticity of elastic boundary and the time-delay effects of viscous boundary.