Acoustic analysis of anisotropic poroelastic multilayered systems

Abstract

The proposed method allows for an extended analysis of the wave analysis, internal powers, and acoustic performance of anisotropic poroelastic media within semi-infinite multilayered systems under arbitrary excitation. Based on a plane wave expansion, the solution is derived from a first order partial derivative as proposed by Stroh. This allows for an in-depth analysis of the mechanisms controlling the acoustic behaviour in terms of internal powers and wave properties in the media. In particular, the proposed approach is used to highlight the influence of the phenomena intrinsic to anisotropic poroelastic media, such as compression-shear coupling related to the material alignment, the frequency shift of the fundamental resonance, or the appearance of particular geometrical coincidences in multilayered systems with such materials.

Derivation of the state matrix for dynamic analysis of linear homogeneous media

“…By isolating the non-zero eigenvalues and eigenvectors, the state matrix is derived through a series of projections on the computed eigenvectors. As a validation, the terms of the state matrix computed using the proposed method have been compared to the results in Parra Martinez et al, 5 and found to be equal within the numerical precision.…”

“…In a recent paper, 5 the authors proposed a method to model the acoustics of fully anisotropic poroelastic multilayered systems. A crucial step in the derivation was to determine the state matrix a, and was shown to involve a succession of tedious manipulations of the governing equations.…”

A review of the different approaches to predict the sound transmission loss of building partitions

“…It is also possible to account for the anisotropy of porous materials. 89,90 Besides, as shown by Atalla and Sgard, 91 also perforated plates and screens can be easily modelled as a porous medium. The TMM method offers an easy implementation, described in detail in Chapter 11 of Allard and Atalla, 50 and has a wider applicability compared to the analytical approaches previously described, since it allows the modelling of composite systems made of a variable number of layers, considering media of different natures.…”

A transverse isotropic equivalent fluid model combining both limp and rigid frame behaviors for fibrous materials

“…is the discriminant of the quadratic equation (19). Propagation constant for guided modes are then found explicitly as…”

“…From a computational point of view, Biot's equations can be solved by the finite element method 16,17 (see also the references therein). In some situations, semi-analytical techniques such as the Transfer Matrix Method 18 and the plane wave decomposition 19 can also be used. In these papers, it is illustrated how the anisotropic nature of the material can have a strong impact on sound absorbing properties.…”