Source signature and elastic waves in a half-space under a semicircular source of a nonuniformly spatially distributed impulsive load

Abstract

The half-space elastic response to a source of a nonuniformly spatially distributed impulsive 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 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 axis of symmetry of the half-space and then descends smoothly to zero at the stress-free surface of the half-space. In an earlier work, the author gave an analytical-numerical method for transient multicurvilinear dimensional boundary-value problems and its employment to the present problem. Here, the resultant transient deformation of the half-space 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 called here 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.

Source signature and elastic waves in a half‐space under a sustainable line‐concentrated impulsive normal force

“…While the need for the wave system is commonly recognized, the need for the source signature (introduced in Reference [6]) is not well-known. Whereas the wave fronts can be identified in waveform plots (time history plots) as well as in the snapshot plots (contour plots) of the strained half-space, the source signature can be detected only in the latter.…”

“…Such a transient initial boundary-value problem is the ideal elastic half-space subjected to an abrupt normal line load. It was shown that the half-space response is hypersensitive to the type of loading, to the way it is distributed on the source rim, and to the geometry of the source rim under the load (see also References [1,6]). It is impossible to predict the form of the wave system and the source signature prior to the solution, even when the source in question shares the same load resultant of a previously solved boundary-value problem.…”

“…Since the former is pivotal in the determination of the wave system, the source signature of the present transient boundary-value problem is determined first. The excitation source of Reference [6] consisted of a finite semi-circular canyon embedded in the surface of the half-space under a radial normal Heaviside step-function load. As a result, the source signature appeared as rays across which discontinuities occurred in the dependent variables.…”

“…What is well-known is the need for the wave system; what is not known is the need also for the source signature that is equally crucial in defining the spatial deformation at a given instant of time as well as pivotal in the formation of the wave fronts and their spatial breadth. The source signature is defined as the imprint of the spatiotemporal configuration of the excitation source in the entire material motion of the strained body in question at a given instant of time [6].…”

“…Here, this method is demonstrated via the plane-strain transient boundary-value problem concerning an ideal elastic half-space subjected to a sustaining line-concentrated impulsive normal force applied along a line drawn on the surface of the half-space [3][4][5]. Furthermore, it is intended to formulate the source signature [6] and the wave system, both which exist in the solution, and to describe their role in the critical features of the response of the half-space. To predict the critical events of the deformation, it is necessary to identify explicitly both the source signature and the wave system as they propagate in the strained half-space.…”