On the generation of homogeneous, inhomogeneous and goodier-bishop elastic waves from the geometrical ray theory (2023)
In this paper, a new group of exact and asymptotic analytical solutions of the displacement equation in a homogeneous elastic media, considering the most general solution of the Helmholtz equation, which have not been shown in papers and standard texts, are presented. Moreover, the authors show from the ray theory point of view the meaning of such solutions. These solutions could be helpful in future conceptual works about generation and emerging phenomena in elastic waves such as scattering and diffraction, among others, specifically in the analysis of the boundary conditions. Here, new kinds of P-S body waves that oscillate elliptically and propagate outward from sources in a full-space are found where, as special cases, the grazing longitudinal (Py) and transversal (SVy) waves of the Goodier-Bishop type, the analytic expressions for the Rayleigh wave and surface P waves, for which the amplitude decays from sources, are obtained. Also, the standard expressions for the homogeneous plane wavefronts, surface P waves, and Rayleigh surface waves, are achieved. © 2006-2015 Asian Research Publishing Network (ARPN).