Mathematical model for Rayleigh-type and Love-type wave propagation in pre-stressed composite medium with sinusoidal type of curved boundaries

Abstract

• Rayleigh-type and Love-type wave propagation in reinforced media are studied. • The effect of curved boundaries on the displacement components is investigated. • The boundary is of sinusoidal type with small but non-zero curvature. • Graphs show the effect of curved boundaries and initial stresses on displacements. The aim of this paper is to establish the effect of curved boundaries with small but non-zero curvature on the displacement of a particle due to surface wave propagation in an important geo-media called reinforced composite media. The analysis has been carried out from an unusual stand point, which is to consider the effect of curved boundaries on displacement components during wave propagation. If the displacement components arising for stratified boundaries are termed as primary components, then secondary components should also exist for the curvature present in the boundaries. These secondary parts are composed of different harmonic components with their amplitudes depending on the extent of curvature of boundaries. Depending upon the shape of the boundaries, the wave numbers of the primary and secondary components relate one another. Graphs have been plotted to observe the effect of curved boundaries and initial stresses on displacement components. The clearly observable differences of the curves plotted for the cases of planar and non-planar boundaries forecast the important findings of this paper.