On the control of propagating acoustic waves in sonic crystals: analytical, numerical and optimization techniques

El control de las propiedades acústicas de los cristales de sonido (CS) necesita del estudio de la distribución de dispersores en la propia estructura y de las propiedades acústicas intrínsecas de dichos dispersores. En este trabajo se presenta un estudio exhaustivo de diferentes distribuciones, así como el estudio de la mejora de las propiedades acústicas de CS constituidos por dispersores con propiedades absorbentes y/o resonantes. Estos dos procedimientos, tanto independientemente como conjuntamente, introducen posibilidades reales para el control de la propagación de ondas acústicas a través de los CS. Desde el punto de vista teórico, la propagación de ondas a través de estructuras periódicas y quasiperiódicas se ha analizado mediante los métodos de la dispersión múltiple, de la expansión en ondas planas y de los elementos finitos. En este trabajo se presenta una novedosa extensión del método de la expansión en ondas planas que permite obtener las relaciones complejas de dispersión para los CS. Esta técnica complementa la información obtenida por los métodos clásicos y permite conocer el comportamiento evanescente de los modos en el interior de las bandas de propagación prohibida del CS, así como de los modos localizados alrededor de posibles defectos puntuales en CS. La necesidad de medidas precisas de las propiedades acústicas de los CS ha provocado el desarrollo de un novedoso sistema tridimensional que sincroniza el movimiento del receptor y la adquisición de señales temporales. Los resultados experimentales obtenidos en este trabajo muestran una gran similitud con los resultados teóricos. La actuación conjunta de distribuciones de dispersores optimizadas y de las propiedades intrínsecas de éstos, se aplica para la generación de dispositivos que presentan un rango amplio de frecuencias atenuadas. Se presenta una alternativa a las barreras acústicas tradicionales basada en CS donde se puede controlar el paso de ondas a su través. Los resultados ayudan a entender correctamente el funcionamiento de los CS para la localización de sonido, y para el guiado y filtrado de ondas acústicas.Romero García, V. (2010). On the control of propagating acoustic waves in sonic crystals: analytical, numerical and optimization techniques [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8982Palanci

Evanescent waves and deaf bands in sonic crystals

The properties of sonic crystals (SC) are theoretically investigated in this work by solving the inverse problem k(¿) using the extended plane wave expansion (EPWE). The solution of the resulting eigenvalue problem gives the complex band structure which takes into account both the propagating and the evanescent modes. In this work we show the complete mathematical formulation of the EPWE for SC and the supercell approximation for its use in both a complete SC and a SC with defects. As an example we show a novel interpretation of the deaf bands in a complete SC in good agreement with multiple scattering simulations. © 2011 Copyright 2011 Author(s).This work was supported by MCI-Secretaria de Estado de Investigacion (Spanish government) and the FEDER funds, under grant MAT2009-09438. LMGR would like to thank the UPV for the grant PAID-00-11. VRG is grateful for the support of "Programa de Contratos Post-Doctorales con Movilidad UPV (CEI-01-11)."Romero García, V.; García Raffi, LM.; Sánchez Pérez, JV. (2011). Evanescent waves and deaf bands in sonic crystals. AIP Advances. 1(4):416011-416019. doi:10.1063/1.3675801S4160114160191

Bright and Gap Solitons in Membrane-Type Acoustic Metamaterials

We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schr\"odinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement

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

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

Multi-resonant scatterers in sonic crystals: Locally multi-resonant acoustic metamaterial

An acoustic metamaterial made of a two-dimensional (2D) periodic array of multi-resonant acoustic scatterers is analyzed both experimentally and theoretically. The building blocks consist of a combination of elastic beams of low-density polyethylene foam (LDPF) with cavities of known area. Elastic resonances of the beams and acoustic resonances of the cavities can be excited by sound producing several attenuation peaks in the low frequency range. Due to this behavior the periodic array with long wavelength multi-resonant structural units can be classified as a locally multi-resonant acoustic metamaterial (LMRAM) with strong dispersion of its effective properties. The results presented in this paper could be used to design effective tunable acoustic filters for the low frequency range. (C) 2012 Elsevier Ltd. All rights reserved.This work was supported by MCI Secretaria de Estado de Investigacion (Spanish government) and FEDER funds, under Grants MAT2009-09438 and MTM2009-14483-C02-02. V.R.G. is grateful for the support of "Programa de Contratos Post-Doctorales con Movilidad UPV (CEI-01-11)". A.K. and O.U. are grateful for the support of EPSRC (UK) through research Grant EP/E063136/1.Romero García, V.; Krynkin, A.; García-Raffi, LM.; Umnova, O.; Sánchez Pérez, JV. (2013). Multi-resonant scatterers in sonic crystals: Locally multi-resonant acoustic metamaterial. Journal of Sound and Vibration. 332(1):184-198. doi:10.1016/j.jsv.2012.08.003S184198332

Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size

[EN] The complex dispersion relations along the main symmetry directions of two-dimensional finite size periodic arrangements of resonant or non-resonant scatterers are recovered by using an extension of the SLaTCoW (Spatial LAplace Transform for COmplex Wavenumber) method. This method relies on the analysis of the spatial Laplace transform instead of the usual spatial Fourier transform of the measured wavefield in the frequency domain. We apply this method to finite dimension square periodic arrangements of both rigid and resonant scatterers embedded in air, i.e., to finite size sonic crystals and finite size acoustic metamaterials, respectively. The main hypothesis considered in this work is the mirror symmetry of the finite structure with respect to its median axis along the analyzed direction. However, we show that the method is robust enough to provide excellent results even if this hypothesis is not fully satisfied. Effectively, a minor asymmetry could be considered as a side effect when the structure is large enough because Laplace transforming the field along the main symmetry directions also implies averaging the field in the perpendicular one. The calculated complex dispersion relations are in excellent agreement with those obtained by an already validated technique, like the Extended Plane Wave Expansion (EPWE). The methodology employed in this work is intended to be directly used for the experimental characterization of real 2D periodic and resonant systems.This article is based on work from COST Action DENORMS CA15125, supported by COST (European Cooperation in Science and Technology).Cebrecos, A.; Romero-García, V.; Groby, JP. (2019). Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size. Applied Sciences. 9(3). https://doi.org/10.3390/app90304789

Overexpression of SepJ alters septal morphology and heterocyst pattern regulated by diffusible signals in Anabaena

Filamentous, N2 -fixing, heterocyst-forming cyanobacteria grow as chains of cells that are connected by septal junctions. In the model organism Anabaena sp. strain PCC 7120, the septal protein SepJ is required for filament integrity, normal intercellular molecular exchange, heterocyst differentiation, and diazotrophic growth. An Anabaena strain overexpressing SepJ made wider septa between vegetative cells than the wild type, which correlated with a more spread location of SepJ in the septa as observed with a SepJ-GFP fusion, and contained an increased number of nanopores, the septal peptidoglycan perforations that likely accommodate septal junctions. The septa between heterocysts and vegetative cells, which are narrow in wild-type Anabaena, were notably enlarged in the SepJ-overexpressing mutant. Intercellular molecular exchange tested with fluorescent tracers was increased for the SepJ-overexpressing strain specifically in the case of calcein transfer between vegetative cells and heterocysts. These results support an association between calcein transfer, SepJ-related septal junctions, and septal peptidoglycan nanopores. Under nitrogen deprivation, the SepJ-overexpressing strain produced an increased number of contiguous heterocysts but a decreased percentage of total heterocysts. These effects were lost or altered in patS and hetN mutant backgrounds, supporting a role of SepJ in the intercellular transfer of regulatory signals for heterocyst differentiationEspaña, Plan nacional de Investigación BFU2014-56757-

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

Iridescent Perfect Absorption in Critically-Coupled Acoustic Metamaterials Using the Transfer Matrix Method

[EN] The absorption performance of a locally-reacting acoustic metamaterial under oblique incidence is studied. The metamaterial is composed of a slotted panel, each slit being loaded by an array of Helmholtz resonators. The system is analytically studied using the transfer matrix method, accounting for the viscothermal losses both in the resonator elements and in the slits, allowing the representation of the reflection coefficient in the complex frequency plane. We show that by tuning the geometry of the metamaterial, perfect absorption peaks can be obtained on demand at selected frequencies and different angles of incidence. When tilting the incidence angle, the peaks of perfect absorption are shifted in frequency, producing an acoustic iridescence effect similar to the optic iridescence achieved by incomplete band gap. Effectively, we show that in this kind of locally-reacting metamaterial, perfect and omnidirectional absorption for a given frequency is impossible to achieve because the metamaterial impedance does not depend on the incidence angle (i.e., the impedance is a locally reacting one). The system is interpreted in the complex frequency plane by analysing the trajectories of the zeros of the reflection coefficient. We show that the trajectories of the zeros do not overlap under oblique incidence, preventing the observation of perfect and omnidirectional absorption in locally reacting metamaterials. Moreover, we show that for any locally resonant material, the absorption in diffuse field takes a maximal value of 0.951, which is achieved by a material showing perfect absorption for an incidence angle of 50.34 degrees.Jimenez, N.; Groby, J.; Pagneux, V.; Romero García, V. (2017). Iridescent Perfect Absorption in Critically-Coupled Acoustic Metamaterials Using the Transfer Matrix Method. Applied Sciences (Basel). 7(6):1-11. doi:10.3390/app7060618S1117

Compact resonant systems for perfect and broadband sound absorption in wide waveguides in transmission problems

[EN] This work deals with wave absorption in reciprocal asymmetric scattering problem by addressing the acoustic problem of compact absorbers for perfect unidirectional absorption, flush mounted to the walls of wide ducts. These absorbers are composed of several side-by-side resonators that are usually of different geometry and thus detuned to yield an asymmetric acoustic response. A simple lumped-element model analysis is performed to link the dependence of the optimal resonators surface impedance, resonance frequency, and losses to the duct cross-sectional area and resonator spacing. This analysis unifies those of several specific configurations into a unique problem. In addition, the impact of the potential evanescent coupling between the resonators, which is usually neglected, is carefully studied. This coupling can have a strong impact especially on the behavior of compact absorbers lining wide ducts. To reduce the evanescent coupling, the resonators should be relatively small and therefore their resonances should be damped, and not arranged by order of increasing or decreasing resonant frequency. Finally, such an absorber is designed and optimized for perfect unidirectional absorption to prove the relevance of the analysis. The absorber is 30 cm long and 5 cm thick and covers a single side of a 14.8 x 15 cm(2) rectangular duct. A mean absorption coefficient of 99% is obtained experimentally between 700 and 800 Hz.The authors acknowledge the financial support from the ANR industrial chair MACIA (ANR-16-CHIN-0002). They also acknowledge the Safran group for supporting and funding this research.Boulvert, J.; Gabard, G.; Romero-García, V.; Groby, J. (2022). Compact resonant systems for perfect and broadband sound absorption in wide waveguides in transmission problems. Scientific Reports. 12(1):1-13. https://doi.org/10.1038/s41598-022-13944-111312