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https://hdl.handle.net/2142/23744
Description
Title
Scattering from imperfect interfaces
Author(s)
Yogeswaren, Elankanayakam
Issue Date
1995
Doctoral Committee Chair(s)
Harris, John G.
Department of Study
Applied Mechanics
Physics, Acoustics
Discipline
Applied Mechanics
Physics, Acoustics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Physics, Acoustics
Language
eng
Abstract
Scattering from an imperfect planar interface between two different elastic media was studied to examine how the signals induced at the transducers by reflected, transmitted and scattered waves are related to the interface properties. Also, the effect of anisotropy on scattering was assessed by evaluating the stress field near the interface crack-tips. An application of the reciprocal identity leads to expressions for the measured transmission and reflection coefficients for the plane wave case and for the confocal transducer case where these coefficients appear as a sum of convolutions between a source parameter and the crack opening displacements at the imperfect interface. The expressions for the measurement model of the confocal imaging system also infer that the signal induced at the transducer arises from an averaging of multiple scattered waves over the transducer aperture. The dominant contribution to this induced signal comes from scattered waves that phase match to the interrogating wave. This study shows that the resolution of a confocal imaging system will depend on such source parameters as operating frequency of the transducers as well as on such scatterer parameters as lengths and spacings of cracks. Plane wave scattering by an imperfect interface between anisotropic materials gives an indication of the peculiarities and the scale of effort involved in attempting to solve problems in these materials. Reflection and transmission at a perfect interface between generally anisotropic media was studied to evaluate the amplitude, the slowness vector, the polarization vector, the group velocity vector and the energy flux associated with each phase produced at the interface. When imperfection in the form of a crack is present at the interface, the endpoint singularities have an additional oscillatory component. Stress intensity factors obtained from an alternate quasi-static formulation were found to be in satisfactory agreement with the wave scattering model values at low frequencies. In performing experiments to assess the interface imperfection in anisotropic materials, the orientation of the plane of experiment relative to the material axes should be chosen carefully as to obtain the optimum signal at the transducer. A general model of scattering of a focused beam at imperfect interfaces in elastic media should account for the additional complexities due to the anisotropy that may be present.
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