Numerical inversion of the Laplace transformation and the solution of the viscoelastic wave equations
"In the numerical inversion of Laplace transform two general techniques of inversion are analyzed; a study of the procedures based on an expansion of f̄(s) by a polynomial in 1/s (Salzer's method) provides accurate results for certain ranges of t. A curvature criterion for the selection of the range of points for polynomial interpolation, and a geometric distribution in this interval markedly improves the range and the degree of accuracy of inversion. The results may be further improved by multiplying f̄(s) by 1/s of 1/s². Other procedures are based on approximation of f̄(t). This investigation includes a general review of the theory, study of the Papoulis method (using a Fourier sine series expansion of f(t)) and the application of a curvature criterion for determination of a distribution factor, Δ. Other techniques, such as those based on expansion of f(t) by other trigonometric sets, Legendre polynomials, Jacobi polynomials, and Laquerre polynomials are briefly analyzed. Papoulis method is adequate for numerical inversion of the L-transform of the viscoelastic wave equations. Numerical solutions are made for complex viscoelastic wave equations. Utilizing the correspondence principle for dynamic problems the generalized equations for plane, spherical and cylindrical viscoelastic wave equations are formulated. The study of the three-and five-element models reveals that their attenuation for steady-state response is proportional to frequency squared for low frequencies and is constant for high frequencies. Transients in three- and five-element models do not predict accurately the behavior of real earth materials, although both give better approximation than the theory of elasticity"--Abstract, page ii-iii.
Clark, George Bromley, 1912-
Davis, Robert L.
Haas, Charles J.
Ho, C. Y. (Chung You), 1933-1988
Lund, Louis H., 1919-1998
Ph. D. in Mining Engineering
University of Missouri--Rolla
xxii, 188 pages
Note about bibliography
Includes bibliographical references (pages 171-174).
© 1969 Abbas Ali Daneshy, All rights reserved.
Dissertation - Open Access
Wave equation -- Numerical solutions
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Daneshy, Abbas Ali, "Numerical inversion of the Laplace transformation and the solution of the viscoelastic wave equations" (1969). Doctoral Dissertations. 2226.