Doctoral Dissertations

Abstract

"In investigating the behavior of waves traveling through cohesive solids, two assumptions are usually made: that the propagating medium is either elastic or viscoelastic, and that the wave is either planar or spherical in form. For small distances from the source of the disturbance the medium can be considered elastic and the wave spherical rather than planar. The assumption of elasticity allows considerable simplification of the mathematical analysis, and assuming a spherical wave form is an acceptable approximation if the initial disturbance is essentially a point source and the propagating medium is nearly homogeneous. However, for large distances from the source of the disturbance, assuming an elastic medium can lead to large errors. Consequently, a viscoelastic medium is often assumed. The mathematics involved in obtaining solutions for even the simplest viscoelastic case, that of a plane wave in a Voigt solid, is generally quite complicated, especially if other than assumed solutions are desired, and is even more so if the wave form is considered as being spherical. For these reasons plane-wave viscoelastic solutions are frequently used in an effort to approximate field observations.

In this investigation solutions of the viscoelastic, plane-wave equations are obtained by means of the Laplace transform for the velocity and strain. The peak velocity vp and peak strain εp are found respectively to vary with the frequency ωo and dimensionless distance X̲ by the relationships

Vp = 0.845X-0.570

and

εp = 0.694X-0.491

The viscoelastic, spherical-wave equation of motion is solved by assuming a steady state solution and is found to be related to an assumed solution for the plane-wave case. Expressions for the displacement potential as a function of real time are obtained by means of the Laplace transform and are expressed as integrals.

Equations of motion for elastic and Voigt viscoelastic spherical waves are derived, and solutions of the equations for the plane and spherical, elastic waves are obtained for comparative purposes with those of the viscoelastic cases”--Abstract, pages ii-iii.

Advisor(s)

Clark, George Bromley, 1912-

Department(s)

Mining Engineering

Degree Name

Ph. D. in Mining Engineering

Publisher

University of Missouri at Rolla

Publication Date

1964

Pagination

v, 46 pages

Note about bibliography

Includes bibliographical references (pages 22-24).

Rights

© 1964 Gerald Bruce Rupert, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 1663

Print OCLC #

5962757

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