Application of the generalized rays to transient waves in an elastic half-space due to a buried line source
type: Item
instance of: scholarly article
title: Application of the generalized rays to transient waves in an elastic half-space due to a buried line source
zbMATH Open document ID: 0611.73028
DOI: 10.1007/BF01182123
published in: Acta Mechanica
publication date: 1987-01-01T00:00:00Z
review text: The aim of this investigation is to study by means of the generalized rays the effects of a free surface on the propagation of elastic transient waves emanating from a line source of explosion, which varies with time as the Heaviside step function with rounded shoulders. This is accomplished by the numerical evaluation and analysis of the exact solutions provided by this theory. Graphs are obtained which show displacements and stresses as functions of time at three different receivers in the interior of an infinite medium and at the free surface of a homogeneous half-space. The character of surface responses, for short observation times, is the same as in the infinite medium, with the difference that they are all amplified (surface receiver effect). The late time surface responses are characterized by the presence of a smooth pulse representing the Rayleigh surface wave. The Rayleigh pulse in the non-vanishing surface stress takes its ultimate shape already close to the epicentre, while the Rayleigh pulse in the surface displacements developes fully at the remote distance from the epicentre.
Mathematics Subject Classification ID: 74M20
Mathematics Subject Classification ID: 74J15
zbMATH DE Number: 3988803
zbMATH Keywords: generalized rays
zbMATH Keywords: free surface
zbMATH Keywords: elastic transient waves
zbMATH Keywords: line source of explosion
zbMATH Keywords: Heaviside step function
zbMATH Keywords: rounded shoulders
zbMATH Keywords: numerical evaluation
zbMATH Keywords: exact solutions
zbMATH Keywords: surface responses
zbMATH Keywords: Rayleigh pulse
zbMATH Keywords: non- vanishing surface stress
zbMATH Keywords: ultimate shape
author: Piotr Borejko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3988803