Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems

The limits of flexural wave absorption by open lossy resonators are analytically and numerically reported in this work for both the reflection and transmission problems. An experimental validation for the reflection problem is presented. The reflection and transmission of flexural waves in 1D resonant thin beams are analyzed by means of the transfer matrix method. The hypotheses, on which the analytical model relies, are validated by experimental results. The open lossy resonator, consisting of a finite length beam thinner than the main beam, presents both energy leakage due to the aperture of the resonators to the main beam and inherent losses due to the viscoelastic damping. Wave absorption is found to be limited by the balance between the energy leakage and the inherent losses of the open lossy resonator. The perfect compensation of these two elements is known as the critical coupling condition and can be easily tuned by the geometry of the resonator. On the one hand, the scattering in the reflection problem is represented by the reflection coefficient. A single symmetry of the resonance is used to obtain the critical coupling condition. Therefore the perfect absorption can be obtained in this case. On the other hand, the transmission problem is represented by two eigenvalues of the scattering matrix, representing the symmetric and anti-symmetric parts of the full scattering problem. In the geometry analyzed in this work, only one kind of symmetry can be critically coupled, and therefore, the maximal absorption in the transmission problem is limited to 0.5. The results shown in this work pave the way to the design of resonators for efficient flexural wave absorption

2D ground motion at a soft viscoelastic layer/hard substratum site in response to SH cylindrical seismic waves radiated by deep and shallow line sources

We show, essentially by theoretical means, that for a site with the chosen simple geometry and mechanical properties (horizontal, homogeneous, soft viscoelastic layer of infinite lateral extent overlying, and in welded contact with, a homogeneous, hard elastic substratum of half-infinite radial extent, shear-horizontal motion): 1) coupling to Love modes is all the weaker the farther the seismic source (modeled as a line, assumed to lie in the substratum) is from the lower boundary of the soft layer, 2) for a line source close to the lower boundary of the soft layer, the ground response is characterized by possible beating phenomena, and is of significantly-longer duration than for excitation by cylindrical waves radiated by deep sources. Numerical applications of the theory show, for instance, that a line source, located 40m below the lower boundary of a 60m thick soft layer in a hypothetical Mexico City-like site, radiating a SH pulse of 4s duration, produces substantial ground motion during 200s, with marked beating, at an epicentral distance of 3km. This response is in some respects similar to that observed in real cities located at soft-soil sites so that the model employed herein may help to establish the causes and pinpoint the major contributing factors of the devastating effects of earthquakes in such cities.Comment: Submitted to Geophys.J.Int

A method to determine the acoustic reflection and absorption coefficients of porous media by using modal dispersion in a waveguide

The measurement of acoustic material characteristics using a standard impedance tube method is generally limited to the plane wave regime below the tube cut-on frequency. This implies that the size of the tube and, consequently, the size of the material specimen must remain smaller than a half of the wavelength. This paper presents a method that enables the extension of the frequency range beyond the plane wave regime by at least a factor of 3, so that the size of the material specimen can be much larger than the wavelength. The proposed method is based on measuring of the sound pressure at different axial locations and applying the spatial Fourier transform. A normal mode decomposition approach is used together with an optimization algorithm to minimize the discrepancy between the measured and predicted sound pressure spectra. This allows the frequency and angle dependent reflection and absorption coefficients of the material specimen to be calculated in an extended frequency range. The method has been tested successfully on samples of melamine foam and wood fiber. The measured data are in close agreement with the predictions by the equivalent fluid model for the acoustical properties of porous media

Metadiffusers for quasi-perfect and broadband sound diffusion

Sound diffusion refers to the ability of a surface to evenly scatter sound energy in both time and space. However, omnidirectional radiation of sound, or perfect diffusion, can be impractical or difficult to reach under traditional means. This is due to the considerable size required by, and the lack of tunability, of typical quarter-wavelength scattering strategies necessary for producing the required complexity of the surface acoustic impedance. As such, it can be a challenge to design sound diffusing structures that can display near perfect diffusion performance within slim dimensions. In this work, we propose a method for obtaining quasi-perfect and broadband sound diffusion coefficients using deep-subwavelength acoustic diffusers, i.e., metadiffusers. The relation between the geometry of the metasurface, the bandwidth and the diffusion performance is analytically and numerically studied. For moderate bandwidths, around 1/3 of an octave, the method results in nearly perfect sound diffusion, while for a bandwidth of 2.5 octaves a normalized diffusion coefficient of 0.8 was obtained using panels 1/30th thinner than traditional phase-grating designs. The ratio between the wavelength and the size of the unit cell was identified as a limitation of the performance. This work demonstrates the versatility and effectiveness of metadiffusers to generate diffuse reflections outperforming those of classical sound diffuser

Stealth and equiluminous materials for scattering cancellation and wave diffusion

[EN] We report a procedure to design two-dimensional acoustic structures with prescribed scattering properties. The structures are designed from targeted properties in the reciprocal space so that their structure factors, i.e. their scattering patterns under the Born approximation, exactly follow the desired scattering properties for a set of wavelengths. The structures are made of a distribution of rigid circular cross-sectional cylinders embedded in air. We demonstrate the efficiency of the procedure by designing two-dimensional stealth acoustic materials with broadband back-scattering suppression independent of the angle of incidence and equiluminous acoustic materials exhibiting broadband scattering of equal intensity also independent of the angle of incidence. The scattering intensities are described in terms of both single and multiple scattering formalisms, showing excellent agreement with each other, thus validating the scattering properties of each material.This work has been funded by the project Conseil Regional des Pays de la Loire HYPERMETA under the program Etoiles Montantes of the Region Pays de la Loire, by the project Agence Nationale de la Recherche ANR-RGC METARoom [grant number (ANR-18-CE08-0021)] and by the project PID2020112759GB-I00 of the Ministerio de Ciencia e Innovacion.Kuznetsova, S.; Groby, JP.; García-Raffi, LM.; Romero-García, V. (2021). Stealth and equiluminous materials for scattering cancellation and wave diffusion. Waves in Random and Complex Media. https://doi.org/10.1080/17455030.2021.194863

Digital sound absorbing metafluid inspired by cereal straws

International audienceUsed as building biomaterials for centuries, cereal straws are known for their remarkable acoustic performances in sound absorption. Yet, their use as fibrous media disregards their internal structure made of nodes partitioning stems. Here, we show that such nodes can impart negative acoustic bulk modulus to straw balls when straws are cut on either side of a node. Such metafluid inspired by cereal straws combines visco-thermal diffusion with strong wave dispersion arising from quarter-wavelength resonances within straws. Large spectral bandgaps and slow sound regimes are theoretically predicted and experimental data from impedance tube measurements on an idealised 3D-printed sample layer are in good agreement with the theoretical model. Perfect absorption is achieved at wavelengths 13 times larger than the thickness of the metafluid layer, and slow sound entails an increased density of states causing a cascade of high absorption peaks. Such features could lead cereal straws to serve as cheap acoustic bio-metamaterials

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab.Comment: submitted to Math.Meth.Appl.Sc

Asymptotic limits of some models for sound propagation in porous media and the assignment of the pore characteristic lengths

Modeling of sound propagation in porous media requires the knowledge of several intrinsic material parameters, some of which are difficult or impossible to measure directly, particularly in the case of a porous medium which is composed of pores with a wide range of scales and random interconnections. Four particular parameters which are rarely measured non-acoustically, but used extensively in a number of acoustical models, are the viscous and thermal characteristic lengths, thermal permeability, and Pride parameter. The main purpose of this work is to show how these parameters relate to the pore size distribution which is a routine characteristic measured non-acoustically. This is achieved through the analysis of the asymptotic behavior of four analytical models which have been developed previously to predict the dynamic density and/or compressibility of the equivalent fluid in a porous medium. In this work the models proposed by Johnson, Koplik, and Dashn [J. Fluid Mech. 176, 379–402 (1987)], Champoux and Allard [J. Appl. Phys. 70(4), 1975–1979 (1991)], Pride, Morgan, and Gangi [Phys. Rev. B 47, 4964–4978 (1993)], and Horoshenkov, Attenborough, and Chandler-Wilde [J. Acoust. Soc. Am. 104, 1198–1209 (1998)] are compared. The findings are then used to compare the behavior of the complex dynamic density and compressibility of the fluid in a material pore with uniform and variable cross-section

Metadiffusers : deep-subwavelength sound diffusers

We present deep-subwavelength diffusing surfaces based on acoustic metamaterials, namely metadiffusers. These sound diffusers are rigidly backed slotted panels, with each slit being loaded by an array of Helmholtz resonators. Strong dispersion is produced in the slits and slow sound conditions are induced. Thus, the effective thickness of the panel is lengthened introducing its quarter wavelength resonance in the deep-subwavelength regime. By tuning the geometry of the metamaterial, the reflection coefficient of the panel can be tailored to obtain either a custom reflection phase, moderate or even perfect absorption. Using these concepts, we present ultra-thin diffusers where the geometry of the metadiffuser has been tuned to obtain surfaces with spatially dependent reflection coefficients having uniform magnitude Fourier transforms. Various designs are presented where, quadratic residue, primitive root and ternary sequence diffusers are mimicked by metadiffusers whose thickness are 1/46 to 1/20 times the design wavelength, i.e., between about a twentieth and a tenth of the thickness of traditional designs. Finally, a broadband metadiffuser panel of 3 cm thick was designed using optimization methods for frequencies ranging from 250 Hz to 2 kHz

Stealth and equiluminous materials for scattering cancellation and wave diffusion

We report a procedure to design 2-dimensional acoustic structures with prescribed scattering properties. The structures are designed from targeted properties in the reciprocal space so that their structure factors, i.e., their scattering patterns under the Born approximation, exactly follow the desired scattering properties for a set of wavelengths. The structures are made of a distribution of rigid circular cross-sectional cylinders embedded in air. We demonstrate the efficiency of the procedure by designing 2-dimensional stealth acoustic materials with broadband backscattering suppression independent of the angle of incidence and equiluminous acoustic materials exhibiting broadband scattering of equal intensity also independent of the angle of incidence. The scattering intensities are described in terms of both single and multiple scattering formalisms, showing excellent agreement with each other, thus validating the scattering properties of each material