Source signature and elastic waves in a half-space under a semicircular source of a normal impulsive cosine load

Abstract

The half-space elastic response to a source of a nonuniformly spatially distributed impulsive normal load is presented in this paper. Specifically, an infinite semicircular canyon of a finite radius is embedded in the surface of the half-space where an impulsive cosine load is radially distributed over the entire surface of the canyon. The spatial distribution of this load is such that the load is maximum at the stress-free boundary of the half-space and then descends smoothly to zero at the axis of symmetry of the half-space. In earlier works, the author gave an analytical-numerical method for transient multicurvilinear dimensional boundary-value problems and its employment to nonuniformly spatially distributed loads. Here, the resultant transient deformation of the half-space under a cosine load is described and interpreted. In particular, a detailed discussion is devoted to the appearance of spatially stationary strong discontinuity fronts in the interior of the deformed half-space. These fronts, which disclose the nature of the prescribed source of disturbance, are the source signature. A complete account is then given of the waves emitted from the source signature and those generated by boundary conditions, all revealing themselves explicitly by the solution method.