The rigid ellipsoid in the presence of a low frequency elastic wave
Authors:
George Dassios and Kiriakie Kiriaki
Journal:
Quart. Appl. Math. 43 (1986), 435-456
MSC:
Primary 73D25
DOI:
https://doi.org/10.1090/qam/846156
MathSciNet review:
846156
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Abstract: A longitudinal, or a transverse, plane elastic wave is incident on a rigid triaxial ellipsoid. The zeroth-order and first-order low-frequency approximations are obtained explicitly at every point exterior to the ellipsoid by solving appropriate exterior boundary value problems of potential theory. The normalized scattering amplitudes are evaluated up to the ${k^2}$-order and the leading term of the scattering cross section is given explicitly.
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G. Dassios, Convergent low-frequency expansions for penetrable scatterers, J. Math. Phys. 18, 126 (1977)
G. Dassios, Second order low-frequency scattering by the soft ellipsoid, SIAM J. Appl. Math. 38, 373 (1980)
G. Dassios, Low-frequency scattering theory for a penetrable body with an impenetrable core, SIAM J. Appl. Math. 42, 272 (1982)
G. Dassios, Scattering of acoustic waves by a coated pressure-release ellipsoid, J. Acoust. Soc. Am. 70, 176 (1981)
G. Dassios and K. Kiriaki, The low-frequency theory of elastic wave scattering, Quart. Appl. Math. 42, 225 (1984)
G. Dassios and K. Kiriaki, The ellipsoidal cavity in the presence of a low-frequency elastic wave, Quart. Appl. Math. (1987)
N. G. Einspruch, E. J. Witterholt and R. Truell, Scattering of a plane transverse wave by a spherical obstacle in an elastic medium, J. Appl. Phys. 31, 806 (1960)
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V. D. Kupradze, Dynamical problems in elasticity, Progress in solid mechanics III, North-Holland, 1963
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L. Solomon, Elasticité linéaire, Masson et cie, 1968
V. Twersky, Certain transmission and reflection theorems, J. Appl. Phys. 25, 859 (1954)
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C. F. Ying and R. Truell, Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid, J. Appl. Phys. 27, 1086 (1956)
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Article copyright:
© Copyright 1986
American Mathematical Society