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

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.

A homogenization method used to predict the performance of silencers containing parallel splitters

An analytical model based on a homogenization process is used to predict and understand the behavior of finite length splitter/baffle-type silencers inserted axially into a rigid rectangular duct. Such silencers consist of a succession of parallel baffles made of porous material and airways inserted axially into a rigid duct. The pore network of the porous material in the baffle and the larger pores due to the airway can be considered as a double porosity (DP) medium with well-separated pore sizes. This scale separation leads by homogenization to the DP model, widely used in the porous material community. This alternative approach based on a homogenization process sheds physical insight into the attenuation mechanisms taking place in the silencer. Numerical comparisons with a reference method are used to show that the theory provides good results as long as the pressure wave in the silencer airways propagates as a plane wave parallel to the duct axis. The explicit expression of the axial wavenumber in the DP medium is used to derive an explicit expression for the optimal resistivity value of the porous material, ensuring the best dissipation for a given silencer geometry.

Enhancing the absorption properties of acoustic porous plates by periodically embedding Helmholtz resonators

This paper studies the acoustical properties of hard-backed porous layers with periodically embedded air filled Helmholtz resonators. It is demonstrated that some enhancements in the acoustic absorption coefficient can be achieved in the viscous and inertial regimes at wavelengths much larger than the layer thickness. This enhancement is attributed to the excitation of two specific modes: Helmholtz resonance in the viscous regime and a trapped mode in the inertial regime. The enhancement in the absorption that is attributed to the Helmholtz resonance can be further improved when a small amount of porous material is removed from the resonator necks. In this way the frequency range in which these porous materials exhibit high values of the absorption coefficient can be extended by using Helmholtz resonators with a range of carefully tuned neck lengths.

Multiple scattering in porous media: comparison with water saturated double porosity media

Multiple scattering in a poroelastic medium obeying Biot's theory is studied; the scatterers are parallel identical cylindrical holes pierced at random in the medium. The paper focuses first on the influence, on the effective wavenumbers, of the mode conversions that occur at each scattering event. The effect of the holes on the dispersion curves is then examined for two different values of the ratio of their radius to the pores mean radius. Depending on the latter, the dispersion curves of the pierced material are compared, for the fast and shear waves, with those of either a more porous medium or a double porosity medium.

Tunable sound absorption of silicone rubber materials via mesoporous silica

Mesoporous silica significantly enhanced sound absorption of silicone rubber via prolonging the propagation way and energy dissipated of acoustic wave.