Transmission of longitudinal waves through a plane interface between two dissimilar porous elastic solid half-spaces

An investigation of reflection and transmission phenomena due to incident plane longitudinal waves at a plane interface between two different porous elastic solid half spaces is presented. The theory of elastic medium with voids (pores) developed by Cowin and Nunziato [Linear elastic materials with voids, Journal of Elasticity 13 (1983) 125-147] has been employed to write down the equations of motion and constitutive relations. Reflection and transmission coefficients for limitly low and high frequency longitudinal plane wave incident obliquely at the plane interface have been obtained. In the case of limitly low frequency incident wave, the effect of presence of voids are found significant on reflection and transmission coefficients and there are three reflected and three transmitted waves. For limitly high frequency incident longitudinal wave, the reflection and refraction phenomenon is similar to that of classical elastic theory and no effect of the presence of voids is observed. Partitions of incident energy at the interface have also been discussed. The nature of dependence of reflection and transmission coefficients with angle of incidence have also been studied numerically for a specific model.