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Three-dimensional Green's function and its derivative for materials with general anisotropic magneto-electro-elastic coupling

Federico C. Buroni and Andrés Sáez
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 466, No. 2114 (8 February 2010), pp. 515-537
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/25661451
Page Count: 23
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Three-dimensional Green's function and its derivative for materials with general anisotropic magneto-electro-elastic coupling
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Abstract

Explicit expressions of Green's function and its derivative for three-dimensional infinite solids are presented in this paper. The medium is allowed to exhibit a fully magneto-electro-elastic (MEE) coupling and general anisotropic behaviour. In particular, new explicit expressions for the first-order derivative of Green's function are proposed. The derivation combines extended Stroh formalism, Radon transform and Cauchy's residue theory. In order to cover mathematical degenerate and non-degenerate materials in the Stroh formalism context, a multiple residue scheme is performed. Expressions are explicit in terms of Stroh's eigenvalues, this being a feature of special interest in numerical applications such as boundary element methods. As a particular case, simplifications for MEE materials with transversely isotropic symmetry are derived. Details on the implementation and numerical stability of the proposed solutions for degenerate cases are studied.

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