Modeling and coupling of acoustical layered systems that consist of elements having different transfer matrix dimensions

Abstract

The transfer matrix method that is often used to model layered or lumped acoustical systems was inspired by a classical methodology commonly used in electrical engineering. To take advantage of that procedure’s accuracy and modeling efficiency, the transfer matrix method has been further adapted here to allow coupling of layered acoustic media having different matrix dimensions. For example, in the case of fluid, or effective fluid, media, the acoustic transfer matrix elements are conventionally modeled using two-by-two matrices. In contrast, a four-by-four matrix is required to model an elastic solid layer, and a six-by-six matrix is required to model a poroelastic layer, since multiple wave types propagate within the latter elements. Here, we introduce a modified transfer matrix calculation process that draws on various matrix operations to couple four-by-four and/or six-by-six matrices with the two-by-two matrices of other acoustical elements. The matrix operations include singular value decomposition and QR decomposition. These tools are used to reduce the order of elastic solid or poroelastic layer matrices from four-by-four or six-by-six to two-by-two, respectively, so that a layered system can be modeled simply by multiplying together a sequence of two-by-two matrices representing all the layered acoustic elements regardless of their complexity, thus finally creating an overall two-by-two matrix. In this article, the proposed method is applied to several different layered or multipanel structures, and the predicted acoustical properties are compared to results obtained by using previously-existing methods in order to validate the modified transfer matrix method.