Surface impedance matrices to model the propagation in multilayered media

The surface impedance matrices in stratified plates made of fluid layers and/or anisotropic absorbing solid layers link the particle velocity field to the stress field at any interface. A surface impedance matrix represents the impedance at a given interface of all the layers located between that interface and one boundary of the medium. For each interface, there are two surface impedance matrices, each one corresponding to one boundary. This notion simplifies the computations of the modal solutions. The number of elements in the matrices involved in the computations is divided by a factor of four in comparison to usual matrix methods. This paper describes the method and presents examples to illustrate its interests and its efficiency where other techniques fail, for instance in the case of modes possessing energy in layers embedded in the structure.