A robust transfer matrix formulation for ultrasonic wave propagation in multilayered absorbing media.

Abstract

An improved version of the transfer matrix approach is presented where general expressions are obtained for reflection and transmission coefficients in either fluid or solid half-space and problems associated with numerical stability are solved efficiently. The formulation is applicable to longitudinal and shear input wave alike, at arbitrary incidence angles and for any sequence of solid or fluid layers. Also, allowance is made for viscoelastic behavior by means of relaxation functions and the response to arbitrary incident pulse shapes and beam profiles is obtained through a two-dimensional numerical Laplace inversion. For application to bond quality inspection, the interface between any two layers is handled by introducing a very thin interphase layer, rigidly bonded to its neighbors, with adjustable viscoelastic properties. In the case of a metal–polymer–metal structure, simulations show resonance splitting, which measures coupling strength between layers and is found to be very sensitive to small changes in the interfacial conditions. These theoretical results are confirmed by experiments and good estimates are given for the specific stiffness of the interface region.