26 research outputs found

    General method to retrieve all effective acoustic properties of fully-anisotropic fluid materials in three dimensional space

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    Anisotropic fluid materials are of growing interest with the development of metamaterials and transformation acoustics. In the general three-dimensional case, such materials are characterized by a bulk modulus and a full symmetric matrix of density. Here, a method is presented to retrieve the bulk modulus and all six components of the density matrix from a selected set of six incident plane waves impinging on a layer of the material. From the six components of the density tensor, the three principal directions and the three principal densities of the material are recovered. The approach relies on the analytical expression of the reflection and transmission coefficients derived from a state vector analysis. It results in simple, closed-form, and easily-implementable inverse relations for the material parameters. As an illustration, the case of sound propagation through an orthorhombic lattice of overlapping air-filled ellipsoids is considered, the effective complex and frequency-dependent bulk modulus and density matrix of which are derived from homogenization cell problems and account for viscothermal losses. The retrieval method is then applied to the homogenized layer and results bear testament to its robustness to extract accurately all seven material parameters. This makes possible the characterization and design of anisotropic fluid materials in three dimensions

    Nonlocal boundary conditions for corrugated acoustic metasurface with strong near field interactions

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    The propagation of long-wavelength sound in the presence of a metasurface made by arranging acoustic resonators periodically upon or slightly above an impervious substrate is studied. The method of two-scale asymptotic homogenization is used to derive effective boundary conditions, which account for both the surface corrugation and the low-frequency resonance. This method is applied to periodic arrays of resonators of any shape operating in the long-wavelength regime. The approach relies on the existence of a locally periodic boundary layer developed in the vicinity of the metasurface, where strong near-field interactions of the resonators with each other and with the substrate take place. These local effects give rise to an effective surface admittance supplemented by nonlocal contributions from the simple and double gradients of the pressure at the surface. These phenomena are illustrated for the periodic array of cylindrical Helmholtz resonators with an extended inner duct. Effects of the centre-to-centre spacing and orientation of the resonators' opening on the nonlocality and apparent resonance frequency are studied. The model could be used to design metasurfaces with specific effective boundary conditions required for particular applications

    Optimally graded porous material for broadband perfect absorption of sound

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    International audienceThis article presents a numerical optimization procedure of continuous gradient porous layer properties to achieve perfect absorption under normal incidence. This design tool is applied on a graded porous medium composed of a periodic arrangement of ordered unit cells allowing to link the effective acoustic properties to its geometry. The best micro-geometry continuous gradient providing the optimal acoustic reflection and/or transmission is designed via a nonlinear conjugate gradient algorithm. The acoustic performances of the so-designed continuous graded material are discussed with respect to the optimized homogeneous, i.e. non-graded, and monotonically graded material. The numerical results show a shifting of the perfect absorption peak to lower frequencies or a widening of the perfect absorption frequency range for graded materials when compared to uniform ones. The results are validated experimentally on 3D-printed samples therefore confirming the relevance of such gradient along with the efficiency of the control of the entire design process. a) [email protected]

    Introduction to homogenisation theory and its application to porous materials design

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    Invited lectureInternational audienceThis Training school is aimed at the industrial partners and Early Career Investigators. The training will be offered in both theoretical and experimental aspects of developing new sound absorbing and sound controlling structures. During the first day, the refresher training courses will be organised covering the basic theory of sound interaction with porous materials and metamaterials. During the following two days lectures and practical sessions will familiarise the audience with the new methods used in design of conventional and metamaterial based noise reducing treatments

    Extended stress gradient elastodynamics: Wave dispersion and micro-macro identification of parameter

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    International audienceIn its original formulation by Forest & Sab (Math. Mech. Solids, 2017), stress gradient elastodynamics incorporate two inner-lengths to account for size effects in continuum theory. Here, an extended one-dimensional stress gradient model is developed by means of Lagrangian formalism, incorporating an additional inner-length and a fourth-order space derivative in the wave equation. Dispersive properties are characterised and hyperbolicity and stability are proven. Group velocity remains bounded in both original and extended models, proving causality is satisfied for both contrary to a usually-accepted postulate. By means of two-scale asymptotic homogeniza-tion, the high-order wave equation satisfied by the stress gradient model is shown to stand for an effective description of heterogeneous materials in the low-frequency range. An upscaling method is developed to identify the stress gradient material parameters and bulk forces on the parameters of elastic micro-structures. Application of the micro-macro procedure to periodic multi-laminates demonstrates the accuracy of the stress gradient continuum to account for the dispersive features of wave propagation. Frequency and time-domain simulations illustrate these properties

    Complex dispersion relation of surface acoustic waves at a lossy metasurface

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    International audienceThe complex dispersion relation of surface acoustic waves (SAWs) at a lossy resonant metasurface is theoretically and experimentally reported. The metasurface consists of the periodic arrangement of borehole resonators in a rigid substrate. The theoretical model relies on a boundary layer approach that provides the effective metasurface admittance governing the complex dispersion relation in the presence of viscous and thermal losses. The model is experimentally validated by measurements in the semi-anechoic chamber. The complex SAW dispersion relation is experimentally retrieved from the analysis of the spatial Laplace transform of the pressure scanned along a line at the metasurface. The geometrical spreading of the energy from the speaker is accounted for, and both the real and imaginary parts of the SAW wavenumber are obtained. The results show that the strong reduction of the SAW group velocity occurs jointly with a drastic attenuation of the wave, leading to the confinement of the field close to the source and preventing the efficient propagation of such slow-sound surface modes. The method opens perspectives to theoretically predict and experimentally characterize both the dispersion and the attenuation of surface waves at structured surfaces
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