Analysis of reflection and refraction of plane wave at the separating interface of two functionally graded incompressible monoclinic media under initial stress and gravity

Abstract

The present article deals with the reflection and refraction phenomenon of a plane wave at the interface of two distinct functionally (exponentially) graded incompressible monoclinic media in the two separate cases. The first case (Case I) deliberates the influence of initial stress; however, the second case (Case II) analyses the influence of gravity associated with both upper and lower incompressible functionally graded monoclinic media on amplitude ratios of reflected and refracted waves. Two types of waves namely quasi-P and quasi-SV are generated due to the plane wave incident at the common interface of the considered structure. An analytical approach has been employed to compute velocity equations for each of the two cases. The dependency relations of dimensionless amplitude ratio of reflected and refracted waves on various affecting parameters along with angle of incidence have been established in closed form for both the cases. Moreover, the expressions for slowness section have also been derived for the corresponding cases and depicted by the means the graphs. Also as a special case of the problem, the deduced results are validated with the pre-established result. An analysis to unravel the effect of angle of incidence, gravity parameter, material gradient parameter and initial stress associated with lower and upper media on the reflected and refracted waves has also been made meticulously through numerical computations and graphical illustrations. Furthermore, through comparative analysis some important peculiarities in the phenomenon have also been highlighted.