Benoit Nennig

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.

A mode matching method for modeling dissipative silencers lined with poroelastic materials and containing mean flow

A mode matching method for predicting the transmission loss of a cylindrical shaped dissipative silencer partially filled with a poroelastic foam is developed. The model takes into account the solid phase elasticity of the sound-absorbing material, the mounting conditions of the foam, and the presence of a uniform mean flow in the central airway. The novelty of the proposed approach lies in the fact that guided modes of the silencer have a composite nature containing both compressional and shear waves as opposed to classical mode matching methods in which only acoustic pressure waves are present. Results presented demonstrate good agreement with finite element calculations provided a sufficient number of modes are retained. In practice, it is found that the time for computing the transmission loss over a large frequency range takes a few minutes on a personal computer. This makes the present method a reliable tool for tackling dissipative silencers lined with poroelastic materials.

A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions

This work investigates the acoustical properties of a multilayer porous material in which periodic inclusions are embedded. The material is assumed to be backed by a rigid wall. Most of the studies performed in this field used the multipole method and are limited to circular shape inclusions. Here, a mode matching approach, more convenient for a layered system, is adopted. The inclusions can be in the form of rigid scatterers of an arbitrary shape, in the form of an air-filled cavity or in the form of a porous medium with contrasting properties. The computational approach is validated on simple geometries against other numerical schemes and with experimental results obtained in an anechoic room on a rigid grating embedded in a porous material made of 2 mm glass beads. The method is used to study the acoustic absorption behavior of this class of materials in the low frequency range and at a range of angles of incidence.

Using simple shape three-dimensional rigid inclusions to enhance porous layer absorption.

The absorption properties of a metaporous material made of non-resonant simple shape three-dimensional rigid inclusions (cube, cylinder, sphere, cone, and ring torus) embedded in a rigidly backed rigid-frame porous material are studied. A nearly total absorption can be obtained for a frequency lower than the quarter-wavelength resonance frequency due to the excitation of a trapped mode. To be correctly excited, this mode requires a filling fraction larger in three-dimensions than in two-dimensions for purely convex (cube, cylinder, sphere, and cone) shapes. At long wavelengths compared to the spatial period, a cube is found to be the best purely convex inclusion shape to embed in a cubic unit cell, while the embedment of a sphere or a cone cannot lead to an optimal absorption for some porous material properties and dimensions of the unit cell. At a fixed position of purely convex shape inclusion barycenter, the absorption coefficient only depends on the filling fraction and does not depend on the shape below the Bragg frequency arising from the interaction between the inclusion and its image with respect to the rigid backing. The influence of the incidence angle and of the material properties, namely, the flow resistivity is also shown. The results of the modeling are validated experimentally in the case of cubic and cylindrical inclusions.

A displacement-pressure finite element formulation for analyzing the sound transmission in ducted shear flows with finite poroelastic lining

In the present work, the propagation of sound in a lined duct containing sheared mean flow is studied. Walls of the duct are acoustically treated with absorbent poroelastic foams. The propagation of elasto-acoustic waves in the liner is described by Biots model. In the fluid domain, the propagation of sound in a sheared mean flow is governed by the Galbruns equation. The problem is solved using a mixed displacement-pressure finite element formulation in both domains. A 3D implementation of the model has been performed and is illustrated on axisymmetric examples. Convergence and accuracy of the numerical model are shown for the particular case of the modal propagation in a infinite duct containing a uniform flow. Practical examples concerning the sound attenuation through dissipative silencers are discussed. In particular, effects of the refraction effects in the shear layer as well as the mounting conditions of the foam on the transmission loss are shown. The presence of a perforate screen at the air-porous interface is also considered and included in the model.

The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media

Recently Chazot et al. [J. Sound Vib. 332, 1918-1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a certain class of absorbing materials that react like an equivalent fluid. This paper presents an extension of the method to the numerical simulation of Biots waves in poroelastic materials. The technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations. To show the interest of the method for tackling problems of practical interests, poroelastic-acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested. It is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.

Enhancing rigid frame porous layer absorption with three-dimensional periodic irregularities

This papers reports a three-dimensional (3D) extension of the model proposed by Groby et al. [J. Acoust. Soc. Am. 127, 2865-2874 (2010)]. The acoustic properties of a porous layer backed by a rigid plate with periodic rectangular irregularities are investigated. The Johnson-Champoux-Allard model is used to predict the complex bulk modulus and density of the equivalent fluid in the porous material. The method of variable separation is used together with the radiation conditions and Floquet theorem to derive the analytical expression for the acoustic reflection coefficient from the porous layer with 3D inhomogeneities. Finite element method is also used to validate the proposed analytical solution. The theoretical and numerical predictions agree well with the experimental data obtained from an impedance tube experiment. It is shown that the measured acoustic absorption coefficient spectrum exhibits a quasi-total absorption peak at the predicted frequency of the mode trapped in the porous layer. When more than one irregularity per spatial period is considered, additional absorption peaks are observed.

Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption

A theoretical and experimental study of the acoustic absorption of granular porous media made of non-cohesive piles of spherical shells is presented. These shells are either rigid or elastic, possibly drilled with a neck (Helmholtz resonators), and either porous or impervious. A description is given of acoustic propagation through these media using the effective medium models proposed by Johnson (rigid particles) and Boutin (rigid Helmholtz resonators), which are extended to the configurations studied in this work. A solution is given for the local equation of elasticity of a shell coupled to the viscous flow of air through the neck and the micropores. The models and the simulations are compared to absorption spectra measured in reflection in an impedance tube. The effective medium models and the measurements show excellent agreement for configurations made of rigid particles and rigid Helmholtz resonators that induce an additional peak of absorption at low frequency. A shift of the Helmholtz resonance toward low frequencies, due to the softness of the shells is revealed by the experiments for elastic shells made of soft elastomer and is well reproduced by the simulations. It is shown that microporous shells enhance and broaden acoustic absorption compared to stiff or elastic resonators.

Influence of solid phase elasticity in poroelastic liners submitted to grazing flows

In the present work, we study the sound propagation in a duct treated with a poroelastic liner exposed to a grazing flow. Acoustic propagation in the liner and in the fluid domain is respectively governed by Biots model and Galbruns equation. Here, the coupling between Galbruns and Biots equation is carried out with a mixed pressure‐displacement FE. On one hand, a mixed formulation is used in Galbruns equation to avoid numerical locking. And on the other hand, in poroelastic media, the description of both phases involves the displacement of the solid phase and the pressure in the fluid phase. In addition of using the complete Biots model, simplified models are also tested. A fluid equivalent model that does not take into account solid phase elasticity and a model that neglects only the shear stress are hence used. These two simplified models enable to evaluate the contributions of the compressional and shear waves in the solid phase. Finally, validity of each simplified model in the specific case of...

Sound attenuation optimization using metaporous materials tuned on exceptional points

A metamaterial composed of a set of periodic rigid resonant inclusions embedded in a porous lining is investigated to enhance the sound attenuation in an acoustic duct at low frequencies. A transmission loss peak is observed on the measurements and corresponds to the crossing of the lower two Bloch modes of an infinite periodic material. Numerical parametric studies show that the optimum modal attenuation can be achieved at the exceptional point in the parameter plane of inclusion position and frequency, where the two lower modes merge.