Analysis of acoustic properties of multi-layered structures by means of effective acoustic impedance matrix

The effective acoustic impedance matrix [Z(k)] is proposed, and its applications are discussed. After defining [Z (k)], it is shown that [Z(k)] for any kind of multilayered structure can be determined successively from the bottom substrate to the top layer. The use of [Z(k)] obviates some problems often occurring in the numerical calculation of multilayered structures. Using three typical examples, it is shown how [ Z(k)] can be conveniently applied to characterize acoustic wave excitation and propagation in certain complicated layered structures as well as in semi-infinite substrates