Transfer matrix of the sixth order

Abstract

Method of the transfer matrix is used to describe the six-wave diffraction in layered media. The system of differential equations that determine the 6-order transfer matrix is solved by the scaling method with the aid of 6-th order symmetric polynomials. This method is applied to the elastic waves in anisotropic media. Influence of layer thickness and frequency of the wave on the scaling parameter is found. Analytic solutions describing the transfer of thermoelastic waves in isotropic media and elastic stresses in the crystalline layers of the cubic, tetragonal and orthorhombic systems are obtained.

Coefficients of elastic wave's conversion by anisotropic layer

“…Transfer matrix T of the sixth order, according to [5,6] can be calculated by means of the formulas 1 :…”

“…The procedure for computing the matrix A according to (13-14) begins from the choice of the scaling parameter m = 2 j and number N (see formula (13)). These values must satisfy the conditions [5]:…”

“…In the theory of diffraction [2,5] and below in this work T is called transfer matrix. For a homogeneous layer (ρ = const, S gh = const) transfer matrix depends on the matrix W (see formulas (4)) as matrix exponential:…”

“…Usually [3,4] the study of waves in an anisotropic medium is based on the solution of the eigenvalues problem (calculation of the kinematic characteristics, such as velocities of waves) related to the wave equations. The matrix method [5] of solution of wave equations provides a more efficient calculation the amplitudes of the scattered waves. The development and application of this method for conversion coefficients computation is the purpose of this work.…”