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

Abstract

Due to the manufacturing process, some fibrous materials like glasswool may be transversely isotropic (TI): fibers are mostly parallel to a plane of isotropy within which material properties are identical in all directions whereas properties are different along the transverse direction. The behavior of TI fibrous material is well described by the TI Biot's model, but it requires one to measure several mechanical parameters and to solve the TI Biot's equations. This paper presents an equivalent fluid model that can be suitable for TI materials under certain assumptions. It takes the form of a classical wave equation for the pressure involving an effective density tensor combining both limp and rigid frame behaviors of the material. This scalar wave equation is easily amenable to analytical and numerical treatments with a finite element method. Numerical results, based on the proposed model, are compared with experimental results obtained for two configurations with a fibrous material. The first concerns the absorption of an incident plane wave impinging on a fibrous slab and the second corresponds to the transmission loss of a splitter-type silencer in a duct. Both configurations highlight the effect of the sample orientation and give an illustration of the unusual TI behavior for fluids.

Acoustic Properties Study of Anisotropic Porous Materials Through the Biot Model Applied with a Finite Element Model

“…In the case of glass wool, the model can consider a specific scenario of anisotropy such as transversely isotropic (TI) properties. As Nennig indicates [6,15], the equivalent bulk modulus in the JCA model of a TI fluid, will not be affected by anisotropy, therefore yields…”

“…A semi phenomenological equivalent fluid model, the Johnson-Champoux-Allard (JCA) [5,6,11,15] model, and a diphasic model, the Biot-Allard [4,6] model (denoted Biot hereafter) are used for describing the wave propagation. The JCA model yields an equivalent density ρ eq and equivalent bulk modulus K. The Biot model yields the characteristic impedance Z c and the complex wavenumber k. These four properties (ρ eq , K, Z c , k) can be used to calculate the sound absorption coefficients α.…”

“…The JCA model [5,6,11,15] is an equivalent fluid model, which considers the frame or skeleton as motionless and only models the motion in the fluid phase. It is used to describe the visco thermal dissipative effects through five parameters from the porous material: porosity ϕ, specific airflow resistivity r, tortuosity α ∞ , viscous characteristic length Λ, and thermal characteristic length Λ ′ .…”

“…The aim of this paper is to assess the impact of the anisotropy of these parameters, using information from a glass wool sample [15]. The consequence of it is building a strong base that helps put together both models and allow to include the anisotropy of any parameters needed in further investigations.…”

Acoustic wave propagation in effective graded fully anisotropic fluid layers

“…Recent work 6 have shown that anisotropic materials can have different apparent sound speed depending on the direction of propagation, coupling viscous and inertial regimes. This is especially visible at grazing angles of incidence, and can be exploited for absorption considering a diffuse field where all incidences are accounted for.…”