Reflection and transmission through a microstructured slab sandwiched by two half-spaces

Abstract

Abstract The reflection and transmission of a plane wave through a microstructured slab sandwiched by two half-spaces are studied in this paper. First, the wave propagation in a micro-structured solid of the dipolar gradient elasticity is formulated. Then, the reflection and transmission properties of a plane wave through a micro-structured slab sandwiched by two half-spaces are considered. The nontraditional interfacial conditions by requiring the auxiliary monopolar tractions, the auxiliary dipolar tractions, the displacements and the normal derivative of displacements continuous across the two interfaces are used to determine the amplitude ratio. The energy fluxes carried by various waves and the reflection and transmission coefficients in terms of energy flux ratio with respect to incident wave are calculated numerically. Based on these numerical results, the microstructure effects on the reflection and transmission waves for the incident P wave and incident SH wave with different wavelength are discussed. In particular, the influences of three characteristic lengths, namely, the incident wavelength, the thickness of slab and the characteristic length of microstructure, on the reflection and transmission waves are analyzed. It is found that the microstructure effect results in the appearance of evanescent wave mode. The reflection and transmission coefficients are evidently dependent upon the microstructure parameters and become more pronounced when the incident wavelength is close to the characteristic length of microstructure.