The reflection phenomena of plane waves at a free boundary in a prestressed elastic half‐space

Abstract

In this article the reflection phenomena of plane harmonic elastic waves in a homogeneous, prestressed, orthotropic half‐space are discussed. It has been observed that the reflection phenomena of pure mode of P and SV waves in such a medium are different from that of the classical isotropic elastic medium. Apart from the directions parallel to the coordinate axes in the medium there exists a specific direction along which pure modes of P and SV waves may propagate through the medium. It is seen that under certain conditions the P wave propagating in a specific direction will give rise to a reflected wave which is either the superposition of both P and SV waves or an SV wave only, obeying the simple laws of reflection, but it cannot give rise to a pure P mode only. [This phenomenon, i.e., case 3 (as discussed in the paper) may be possible when the denominator of R2 is zero.] Similar phenomena are also observed in the case of an SV wave. Since initial stress generally induces orthotropy in an isotropic medium, similar reflection phenomena should also be observed in a stressfree orthotropic medium. But the reflection pehnomenon of an SH wave is similar to that in the classical elastic medium. Moreover, under equal normal initial stresses, the medium behaves like a classical isotropic one and hence the reflection phenomena are similar to that of the classical case.