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

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

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

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

Experimental validation of deep-subwavelength diffusion by acoustic metadiffusers

International audienceAn acoustic metadiffuser is a subwavelength locally resonant surface relying on slow sound propagation. Its design consists of rigidly backed slotted panels, with each slit being loaded by an array of Helmholtz resonators (HRs). Due to the slow sound properties, the effective thickness of the panel can therefore be dramatically reduced when compared to traditional diffusers made of quarter-wavelength resonators. The aim of this work is to experimentally validate the concept of metadiffusers from the scattering measurements of a specific metadiffuser design, i.e., a Quadratic Residue Metadiffuser (QRM). The experimental results reported herein are in a close agreement with analytical and numerical predictions, therefore showing the potential of metadiffusers for controlling sound diffusion at very low frequencies

Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems

[EN] Perfect, broadband and asymmetric sound absorption is theoretically, numerically and experimentally reported by using subwavelength thickness panels in a transmission problem. The panels are composed of a periodic array of varying crosssection waveguides, each of them being loaded by Helmholtz resonators (HRs) with graded dimensions. The low cut-off frequency of the absorption band is fixed by the resonance frequency of the deepest HR, that reduces drastically the transmission. The preceding HR is designed with a slightly higher resonance frequency with a geometry that allows the impedance matching to the surrounding medium. Therefore, reflection vanishes and the structure is critically coupled. This results in perfect sound absorption at a single frequency. We report perfect absorption at 300¿Hz for a structure whose thickness is 40 times smaller than the wavelength. Moreover, this process is repeated by adding HRs to the waveguide, each of them with a higher resonance frequency than the preceding one. Using this frequency cascade effect, we report quasi-perfect sound absorption over almost two frequency octaves ranging from 300 to 1000¿Hz for a panel composed of 9 resonators with a total thickness of 11¿cm, i.e., 10 times smaller than the wavelength at 300¿Hz.The authors acknowledge fnancial support from the Metaudible Project No. ANR-13-BS09-0003, cofunded by ANR and FRAE.Jimenez, N.; Romero García, V.; Pagneux, V.; Groby, J. (2017). Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems. Scientific Reports. 7(1). doi:10.1038/s41598-017-13706-4S1359571Zheludev, N. I. & Kivshar, Y. S. From metamaterials to metadevices. Nature materials 11, 917–924 (2012).Ding, Y., Liu, Z., Qiu, C. & Shi, J. Metamaterial with simultaneously negative bulk modulus and mass density. 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The use of slow waves to design simple sound absorbing materials. J. Appl. Phys. 117, 124903 (2015).Groby, J.-P., Pommier, R. & Aurégan, Y. Use of slow sound to design perfect and broadband passive sound absorbing materials. J. Acoust. Soc. Am. 139, 1660–1671 (2016).Li, Y. & Assouar, B. M. Acoustic metasurface-based perfect absorber with deep subwavelength thickness. Appl. Phys. Lett. 108, 063502 (2016).Romero-García, V., Theocharis, G., Richoux, O. & Pagneux, V. Use of complex frequency plane to design broadband and sub-wavelength absorbers. The Journal of the Acoustical Society of America 139, 3395–3403 (2016).Jiménez, N., Huang, W., Romero-García, V., Pagneux, V. & Groby, J.-P. Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption. Applied Physics Letters 109, 121902 (2016).Jiménez, N., Romero-García, V., Pagneux, V. & Groby, J.-P. Quasiperfect absorption by subwavelength acoustic panels in transmission using accumulation of resonances due to slow sound. Phys. Rev. B 95, 014205 (2017).Achilleos, V., Theocharis, G., Richoux, O. & Pagneux, V. Non-hermitian acoustic metamaterials: Role of exceptional points in sound absorption. Physical Review B 95, 144303 (2017).Santillán, A. & Bozhevolnyi, S. I. Acoustic transparency and slow sound using detuned acoustic resonators. Phys. Rev. B 84, 064304 (2011).Chong, Y., Ge, L., Cao, H. & Stone, A. D. Coherent perfect absorbers: time-reversed lasers. Physical review letters 105, 053901 (2010).Wan, W. et al. Time-reversed lasing and interferometric control of absorption. Science 331, 889–892 (2011).Groby, J.-P., Duclos, A., Dazel, O., Boeckx, L. & Lauriks, W. Absorption of a rigid frame porous layer with periodic circular inclusions backed by a periodic grating. J. Acoust. Soc. Am. 129, 3035–3046 (2011).Lagarrigue, C., Groby, J., Tournat, V., Dazel, O. & Umnova, O. Absorption of sound by porous layers with embedded periodic arrays of resonant inclusions. J. Acoust. Soc. 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Experimental evidence of a hiding zone in a density-near-zero acoustic metamaterial

[EN] This paper examines the feasibility of cloaking an obstacle using Plate-type Acoustic Metamaterials (PAMs). We present two distinct strategies to cloak this obstacle, using either the near-zero-density regime of a periodic arrangement of plates or the acoustic doping phenomenon to achieve simultaneous zero-phase propagation and impedance matching. The strong limitations induced by viscothermal and viscoelastic losses that cannot be avoided in such a system are studied. A hiding zone is reported analytically, numerically, and experimentally. In contrast to cloaking, where zero-phase propagation must be accompanied by total transmission and zero reflection, the hiding configuration requires that the scattering properties of the hiding device must not be affected by the presence of the obstacle embedded in it. Contrary to cloaking, the hiding phenomenon is achievable even with a realistic PAM possessing unavoidable losses.This article is based upon the work from COST Action DENORMS (No. CA15125), supported by COST (European Cooperation). The authors would like to thank the support of the ANR-RGC METARoom (No. ANR-18-CE08-0021) project. J. Christensen acknowledges the support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramon y Cajal Grant (No. RYC-2015-17156).Malléjac, M.; Merkel, A.; Sánchez-Dehesa Moreno-Cid, J.; Christensen, J.; Tournat, V.; Romero-García, V.; Groby, J. (2021). Experimental evidence of a hiding zone in a density-near-zero acoustic metamaterial. Journal of Applied Physics. 129(14):1-9. https://doi.org/10.1063/5.0042383S191291

Natural sonic crystal absorber constituted of seagrass (Posidonia Oceanica) fibrous spheres

[EN] We present a 3-dimensional fully natural sonic crystal composed of spherical aggregates of fibers (called Aegagropilae) resulting from the decomposition of Posidonia Oceanica. The fiber network is first acoustically characterized, providing insights on this natural fiber entanglement due to turbulent flow. The Aegagropilae are then arranged on a principal cubic lattice. The band diagram and topology of this structure are analyzed, notably via Argand representation of its scattering elements. This fully natural sonic crystal exhibits excellent sound absorbing properties and thus represents a sustainable alternative that could outperform conventional acoustic materials.This article is based upon work from COST Action DENORMS CA15125, supported by COST(European Cooperation in Science and Technology). The authors gratefully acknowledge the ANR-RGC METARoom (ANR-18-CE08-0021) project, the project HYPERMETA funded under the program Etoiles Montantes of the Region Pays de la Loire, and the project PID2019-109175GB-C22 funded by the Spanish Ministry of Science and Innovation. N.J. acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities (MICINN) through grant "Juan de la Cierva - Incorporacion" (IJC2018-037897-I). The authors would like to thank V. Pagneux and R. Pico Vila for useful discussions and J. Barber and C. Dordoni for their help in collecting the samples.Barguet, L.; Romero-García, V.; Jimenez, N.; García-Raffi, LM.; Sánchez Morcillo, VJ.; Groby, J. (2021). Natural sonic crystal absorber constituted of seagrass (Posidonia Oceanica) fibrous spheres. Scientific Reports. 11(1):1-8. https://doi.org/10.1038/s41598-020-79982-9S1811

Perfect absorption in mirror-symmetric acoustic metascreens

Mirror-symmetric acoustic metascreens producing perfect absorption independently of the incidence side are theoretically and experimentally reported in this work. The mirror-symmetric resonant building blocks of the metascreen support symmetric and antisymmetric resonances that can be tuned to be at the same frequency (degenerate resonances). The geometry of the building blocks is optimized to critically couple both the symmetric and the antisymmetric resonances at the same frequency allowing perfect absorption of sound from both sides of the metascreen. A hybrid analytical model based on the transfer matrix method and the modal decomposition of the exterior acoustic field is developed to analyze the scattering properties of the metascreen. The resulting geometry is 3D printed and experimentally tested in an impedance tube. Experimental results agree well with the theoretical predictions proving the efficiency of these metascreens for the perfect absorption of sound in the ventilation problems