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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1963
- Accession Number
- AD0403753
Entities
People
- M. Papadopoulos
Organizations
- University of Wisconsin–Madison