Two Studies in Evanescent Wave Propagation (Beam, Acoustic, Gaussian)
Pott, John
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https://hdl.handle.net/2142/71676
Description
Title
Two Studies in Evanescent Wave Propagation (Beam, Acoustic, Gaussian)
Author(s)
Pott, John
Issue Date
1984
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Abstract
Two problems are studied in this dissertation. In the first problem, surface motion, excited by acoustic emissions produced by fracture processes at the edge of a buried, penny-shape crack, are investigated. First, wave-front approximations to the emissions generated by the sudden growth of a tensile crack in the unbounded elastic solid are reviewed. These approximations are then Fourier transformed to give the high-frequency portion of their spectra. Second, time- and frequency-domain approximations to the surface motions excited by this growing crack, when it is buried in a half-space, are calculated. These results are then scrutinized to elucidate what part of the signals measured at the surface carry information about the crack's size, its orientation, and the fracture processes near the crack-tip.
In the second problem, the reflection and refraction at a fluid-solid interface of an acoustic beam, whose amplitude is Gaussian in cross-section and which oscillates harmonically in time, is studied. The incident and scattered beams are constructed using the complex source-point method. The incident beam is specularly reflected except at angles near one of the critical angles, of which the Rayleigh angle is the most important. Near this angle the beam excites both a leaky Rayleigh wave and a reflected beam, and the interference between these two disturbances produces the beam-shifting noted by other workers. Surprisingly, a backward-travelling leaky Rayleigh wave is also excited, though its amplitude is quite small. The incident beam, near normal incidence, is refracted into a compressional beam and a shear beam, both of whose amplitudes are Gaussian in cross-section. Whereas the incident beam has a circularly shaped cross-section, both transmitted beams have elliptically shaped cross-sections. Moreover, the transmitted beams spread rapidly so that the compressional and shear beams always overlap.
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