Abstract
A harmonic wave of a fixed frequency propagates across the periodic system of elastic layers. The elementary cell consists of three layers. The transfer matrix M may be expressed by two real parameters ϕ, ψ and a set P of 64 further scalar parameters M = M(ϕ, ψ, P). The parameters are uniquely defined for the particular M and may be calculated from a system of trigonometrical equations. It has been proved numerically that, for materials and dimensions given in advance, this function for each integer n satisfies the identity [M (ϕ, ψ, P)]n = M (nϕ, nψ, P). The derived identity drastically simplifies the calculation of displacements and stresses in the periodically layered medium.
References
Z. WESOŁOWSKI, Wave speeds in periodic elastic layers, Arch. Mech., 43, 2-3, 271-286, 1991.
Z. WESOŁOWSKI, Algebra of the transfer matrix for layered elastic material, Arch. Mech., 45, 2, 191-210, 1993.
Z. WESOŁOWSKI, Products of the transition matrices governing the dynamics of set of elastic layers, Bull. Pol. Acad. Sci., Math., 40, 1, 53-57, 1992.
Z. WESOŁOWSKI, Algebra of the transfer matrix for layered elastic material, Arch. Mech., 45, 2, 191-210, 1993.
Z. WESOŁOWSKI, Products of the transition matrices governing the dynamics of set of elastic layers, Bull. Pol. Acad. Sci., Math., 40, 1, 53-57, 1992.
