Reflection and transmission of SH waves at a very rough interface and its band gaps

This paper deals with the reflection and transmission of SH waves at a very rough interface separating two dissimilar isotropic elastic solids. The interface oscillates between two straight lines. By means of homogenization, the domain containing the very rough interface is replaced by an effective material layer whose elastic constants depend on the thickness variable. The reflection and transmission of SH waves at the very rough interface is then reduced to the ones at a FGM layer. The exact analytical formulas for the reflection and transmission coefficients have been derived. Based on them, the dependence of the reflection and transmission coefficients on the incident angle, the wave frequency, the material constants and the geometry of the rough interface are examined. Remarkably, it has been shown that a very rough interface of comb-type with the comb-tooth width varying periodically can produce band-gaps to SH waves. With this fact, many potential applications can be expected coming from very rough interfaces of comb-type with periodic comb-tooth width. It is also shown that the width and the location of band-gaps depend strongly on the contrast of rigidities of two half-spaces, the amplitude of the variation of the comb-tooth width, the incident angle of SH waves and the number of periods of comb-tooth.