Reflection and Transmission of Rayleigh Waves in a Wedge?II

Abstract

Summary The problem of the reflection and transmission of Rayleigh waves in an elastic wedge discussed in an earlier paper for the case of incidence from infinity is now studied in more detail and for the more general case of an incidence from a finite distance from the corner. A detailed application is made of the effect of the critical regions of Rayleigh waves in Lamb's half-space problem when a series of interactions with the wedge faces are considered. These interactions are two-fold, viz. those due to the inwardly progressing waves and those due to the outwardly receding waves. Both lead to contributions given by certain integral equations. While in the latter case the integral equations behave like the Fredholm equations, in the case of the former the behaviour is like Volterra equations of second kind at lower range of wedge angles and like the Fredholm equations at higher range and there is a mixed character in the intermediate values. These approximations lead to dividing the range of the wedge angle, which we take to be from 0 to 180, into five parts at points depending on the critical angles of Lamb's problem. The solutions in these parts are piecewise continuous. A brief outline of the corner wave effects is also included. The numerical results show that the present theory can explain well some of the important experimental features of the problem that were only partially achieved by previous theories. 1. Introduction In a previous part of this work Viswanathan, Kuo & Lapwood (1971) showed that the problem of the reflection and transmission of Rayleigh waves in an elastic wedge is significantly influenced by the actual regions in which these waves can exist in the more fundamental problem of a half-space with a source usually known as the Lamb's problem. In the above work which we refer to as Part I henceforth, we treated the case when the incident field was from infinity. Moreover, the effects of the critical regions for the existence of Rayleigh waves defined in the context of the Lamb's problem were only partially incorporated while dealing with the interactions with the wedge boundaries. In particular such effects were not applied to the waves that travel towards the corner. The purpose of the present work is to study the more general case when the source of the initial Rayleigh field lies at a finite distance 1 from the corner. Further, we