Doctoral Dissertations


"Elastodynamic multipole theory, the theory of least squares, and the theory of integral representation of solutions are employed in solving certain problems involving an elastic solid containing a source and a scatterer. Both the source and scatterer are of finite geometrical extent; they occupy non-intersecting regions. The source is separable, i.e., its mathematical specification consists of an arbitrary vector function of position multiplied by a time function, which is further assumed to be a sinusoid. The scatterer emphasized is a finite void cavity of arbitrary shape; however, scatterers composed of rigid material may also be treated. The calculation of a Green's Function is emphasized; in this case the fields incident upon the scatterer are dipole fields. However, the method presented is amenable to arbitrary specification of the incident field; plane wave scattering is discussed as an example. While scattering from a single object is emphasized, the case where two or more scatterers exist is discussed briefly. The so-called cavity-source problem is also discussed briefly. In all cases, a first approximation to the solution in the form of a linear combination of multipole fields is derived using least squares. An improvement in this approximation is derived using an integral representation of the exact solution. The second and final approximation is in the form of a multipole series in which the terms are the fields of fundamental force systems, i.e., dipoles, quadrupoles, etc"--Abstract, page ii.


Rechtien, Richard D.

Committee Member(s)

Frohlich, Reinhard K.
Penico, Anthony J., 1923-2011
Ziemer, Rodger E.
Bolter, Ernst


Geosciences and Geological and Petroleum Engineering

Degree Name

Ph. D. in Geophysics


University of Missouri--Rolla

Publication Date



xxi, 149 pages

Note about bibliography

Includes bibliographical references (pages 112-113)


© 1972 Jerry Lee Davis, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Elastic solids
Elastic scattering
Electromagnetism -- Mathematical models

Thesis Number

T 2760

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