
Accession Number : AD0684854
Title : ON THE DERIVATION OF SOLUTIONS DUE TO A POINT SOURCE FROM LINE SOURCE RESPONSES,
Corporate Author : CORNELL UNIV ITHACA N Y DEPT OF THEORETICAL AND APPLIED MECHANICS
Personal Author(s) : Thau,Stephen A. ; Pao,YihHsing
Report Date : FEB 1969
Pagination or Media Count : 31
Abstract : A sequence of linear, mathematical operations are derived which transform the generalized function representing a concentrated line source into the generalized function representing an axisymmetric point source. Geometrically, the transformation consists of superposing the derivatives of the Hilbert transforms of line sources in all azimuths through a given point, to produce a concentrated source at that point. Thus, for linear systems the response due to a point source can be deduced from that due to line sources by the same operations. Conditions for which the transformation becomes useful and various alternate forms of the transformation, with examples, are also given. (Author)
Descriptors : (*CONTINUUM MECHANICS, TRANSFORMATIONS(MATHEMATICS)), LINEAR SYSTEMS, BOUNDARY VALUE PROBLEMS, INTEGRAL TRANSFORMS, GEOMETRY, WAVE FUNCTIONS, RAYLEIGH WAVES, ELASTIC PROPERTIES, PROPAGATION
Subject Categories : Quantum Theory and Relativity
Distribution Statement : APPROVED FOR PUBLIC RELEASE