Doctoral Dissertations


"A mathematical model of explosive generated waves in rock is needed in many areas of engineering endeavor. Investigations to date have been unsuccessful in obtaining a model that satisfactorily represents real wave phenomena at all radial distances and in all of the important characteristics.

In this investigation, spherical waves in elastic and Voigt media were investigated. Series solutions for plane waves in a three-element viscoelastic medium were obtained. A dual exponential pressure pulse, P(t) = Po (e-αt-e-ßt) was assumed because it can exhibit significant features of real pressure pulses while avoiding instantaneous rise time, which is an objectionable feature of some of the models frequently employed in the literature.

The most significant correlation of elastic and real waves was their similar decay rates for peak values of particle velocity and displacement at large radial distances. At intermediate distances, Voigt waves exhibited pulse lengthening and peak value attenuation rates similar to those reported for real waves, but the arrival time was much too early.

It was concluded that elastic and Voigt spherical waves, and three-element viscoelastic plane waves are not sufficient to represent explosive generated waves in rock. On the basis of this and other investigations cited in the literature it appears that a mechanism for attenuation other than, or in addition to, viscosity will be needed to satisfactorily represent waves in rock"--Abstract, page ii.


Clark, George Bromley, 1912-

Committee Member(s)

Hansen, Peter G., 1927-2010
Antle, Charles E.
Davidson, Robert F., 1911-1971



Degree Name

Ph. D. in Physics


University of Missouri at Rolla

Publication Date



xvii, 126 pages

Note about bibliography

Includes bibliographical references (pages 96-100).


© 1967 Edward Eugene Hornsey, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Elastic waves
Viscoelasticity -- Mathematical models

Thesis Number

T 2024

Print OCLC #


Electronic OCLC #


Included in

Physics Commons