Accession Number : AD0714992
Title : Investigation of Plane and Spherical Waves in Elastic, Maxwell and Generalized Voigt Solids.
Descriptive Note : Final rept. 1 Feb 66-1 May 70,
Corporate Author : MISSOURI UNIV ROLLA ROCK MECHANICS AND EXPLOSIVES RESEARCH CENTER
Personal Author(s) : Clark,George B.
Report Date : NOV 1970
Pagination or Media Count : 267
Abstract : An investigation of mathematical models of pressure pulses determined the dual exponential, P sub o(e to the power (-alpha t) - e to the power (-beta t)), to be the most versatile in approximating explosively generated pulses. Spherical elastic wave forms as functions of various pressure forcing functions were obtained by Laplace transforms. The expansion of Laplace transforms as the product of a double series and inversion term by term provided more general solutions to the spherical Voigt wave than have been obtained before, as Poisson's ratio was not restricted to 0.25. An extension of the double series product inversion technique to that of a triple series product proved adequate for obtaining plane wave solutions to a three element viscoelastic model. Simpson's rule provided numerical values for integral solutions of the spherical Maxwell wave equations. The inversion of solutions of four generalized spherical Voigt models was accomplished by the application of Bellmans numerical quadrature. A review and comparison of numerical methods of Laplace transform inversions lead to the development of a criterion by which the accuracy may be improved. (Author)
Descriptors : (*DETONATION WAVES, MATHEMATICAL MODELS), (*ROCK, *VISCOELASTICITY), MECHANICAL WAVES, PARTIAL DIFFERENTIAL EQUATIONS, EXPONENTIAL FUNCTIONS, SERIES(MATHEMATICS), INTEGRAL EQUATIONS, WAVE FUNCTIONS, CURVE FITTING, GRAPHICS, CONVERGENCE, BOUNDARY VALUE PROBLEMS, PLASTICS
Subject Categories : Geology, Geochemistry and Mineralogy
Distribution Statement : APPROVED FOR PUBLIC RELEASE