THE USE OF SINGULAR INTEGRALS IN WAVE PROPAGATION PROBLITH APPLICATION TO THE POINT SOURCE IN A SEMI-INFINITE ELASTIC MEDIUM

Abstract

The field due to a general point source of energy in an isotropic, elastic solid with a free surface is investigated. The development of new plane wave representations for the fundamental solutions of elastodynamics is reported. There are two types of situation involved; one is the simpler type involved in the case of a steady point source which moves steadily with any constant velocity in an elastic medium, this type involves superposition of plane waves with respect to a single parameter; the other is the more complicated transient problem in which a point source is set up at a given moment, and thereafter moves at constant velocity, without change of strength. The new representation for the field of a steadily moving source and for the transient source is used in the calculation of fields and displacements in the presence of a free surface. The application of the new approach to the case of a vertical load, to a horizontal load, and to a couple of arbitrary orientation, and the singularities to be expected for the general point source are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1963
Accession Number
AD0403753

Entities

People

  • M. Papadopoulos

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Delta Functions
  • Elastic Waves
  • Equations
  • Geometry
  • Mathematics
  • New York
  • Plane Waves
  • Rayleigh Waves
  • Step Functions
  • Surface Waves
  • Two Dimensional
  • United States
  • Wave Equations
  • Wave Functions
  • Wave Propagation
  • Waves
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.