Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The ellipsoidal cavity in the presence of a low-frequency elastic wave


Authors: George Dassios and Kiriakie Kiriaki
Journal: Quart. Appl. Math. 44 (1987), 709-735
MSC: Primary 73D25
DOI: https://doi.org/10.1090/qam/872823
MathSciNet review: 872823
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Abstract: We consider the problem of scattering of a longitudinal or a transverse plane elastic wave by a general ellipsoidal cavity in the low-frequency region. Explicit closed-form solutions for the zeroth- and first-order approximations are provided in terms of the physical and geometric characteristics of the scatterer, as well as the direction cosines of the incidence and observation points. This was made possible with the introduction of an analytical technique based on the Papkovich representations and their interdependence. The leading low-frequency term for the normalized spherical scattering amplitudes and the scattering cross section are also given explicitly. Degenerate ellipsoids corresponding to the prolate and oblate spheroids, the sphere, the needle, and the disc are considered as special cases.


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DOI: https://doi.org/10.1090/qam/872823
Article copyright: © Copyright 1987 American Mathematical Society


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