Civil Engineering Reference
In-Depth Information
11
Modelling multilayered systems
with porous materials using
the transfer matrix method
11.1
Introduction
The description of the acoustic field in a porous layer is not simple, because the shear
wave and the two compressional waves propagating forward and backward are present.
In a layered medium with porous layers, elastic solid layers and fluid layers, a complete
description can become very involved. A matrix representation of sound propagation,
similar to that used by Brekhovskikh (1960), Folds and Loggins (1977), Scharnhorst
(1983) and Brouard
et al
. (1995) is described in this chapter, and used to model plane
acoustic fields in stratified media. The stratified media are assumed laterally infinite.
They can be of different nature: elastic solid, thin plate, fluid, rigid porous, limp porous
and poroelastic. The presented model is essentially based on the representation of plane
wave propagation in different media, in terms of transfer matrices. The presentation of the
transfer matrix for transversally isotropic porous media has been described in Chapter 10.
However, the presentation in this chapter assumes the different media to be homogeneous
and isotropic. The modelling is general in the sense that it can handle automatically
arbitrary configurations of layered media. The theoretical background behind the transfer
matrix method is first recalled. Next, transfer and coupling matrices of different types of
layer will be given, followed by the algorithm used to solve for the acoustic indicators of
the problem. Finally, basic application examples are presented. Extensions and examples
of advanced applications will be discussed in Chapter 12.
