Response of a multi-layered infinite plate to an oblique plane wave by means of transfer matrices

Abstract

Starting with the basic equations connecting the state variables of normal stress, shear stress, tangential velocity and normal velocity, a transfer matrix for a solid plate has been derived. It has been shown that for the limiting case of normal excitation (tangential wave number equalling zero), this matrix yields a juxtaposition of the uncoupled 2 × 2 matrices corresponding to the normal (longitudinal) waves and transverse shear waves. The general transfer matrix relation has been used, with the boundary conditions of zero shear stress and appropriate radiation loading on the two exposed surfaces, to evaluate the response of the plate to a given external pressure excitation on one of the faces. The resulting expressions tally exactly with those available in the literature. A method has been indicated for evaluation of the overall transfer matrix of a compound wall by incorporating the transfer matrix of a damping layer as a possible constituent of the wall. Expressions for the overall reflection, transmission and absorption of the acoustic power of the obliquely incident plane wave have been obtained in terms of the overall transfer matrix parameters of the compound wall.