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Calculation of the Six-Beam Diffraction in Layered Media Using Polynomials of Principal Minors

Department of Mathematical Modelling and Cybernetics, Syktyvkar State University, Syktyvkar 167001, Oktyabrskii pr. 55, Russia

E-mail Address: ybelyayev@mail.ru

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https://doi.org/10.1142/S2591728518500172Cited by:2 (Source: Crossref)

Abstract

The scattering of plane elastic waves by an anisotropic layered medium in the case of the six-beam diffraction is considered. The matrix method for solving wave equations is developed. The conversion coefficients $C_{i j}$ for the three types of incident waves (horizontally polarized shear wave, vertically polarized shear wave and longitudinal wave) are defined. Representations of coefficients $C_{i j}$ through elements of transfer matrix are found. The method for coefficients $C_{i j}$ calculations is presented. It does not require the solving of algebraic problem on eigenvalues for waves in an anisotropic layer. Some features of the functional dependencies of $C_{i j}$ on the angles of incidence, wave frequency and layer thickness are demonstrated on several examples of the crystals in a three-layer model. It is shown that the conversions SH wave into SV waves and SV wave into SH waves are equivalent.

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