Viscothermal effects in a two-dimensional acoustic black hole: A boundary element approach

[EN] The acoustic analog of the quantum black hole for airborne sound in two dimensions was denominated as an omnidirectional acoustic absorber by Climente et al. [see Appl. Phys. Lett., 100, 144103 (2012)], who characterized its absorbing properties without providing any theoretical support. The viscothermal losses of the underlying structure, which consists of an absorbing core and a surrounding gradient-index (GRIN) lens both made of periodic distributions of cylindrical rods, are here comprehensively studied by using the boundary element method (BEM) in two dimensions. It is shown that the numerical simulations in two dimensions reproduce fairly well the increase in absorption of the core when the GRIN lens is added and reveal that the discrepancy between measured and calculated values of absorbance is an artifact of the experimental setup. The possibility of independent calculation of viscous and thermal losses contributions in the two-dimensional (2D) BEM algorithm is employed for the comparison with a homogenization theory in which the cluster of cylinders is represented by a single fluidlike viscous cylinder with effective parameters. We conclude that viscous losses represent about 90% of the total energy dissipated in the core. The homogenization approach results are only 2% below the results calculated with 2D BEM, indicating that the effective parameters obtained by the homogenization are very accurate.Cutanda-Henríquez, V.; Sánchez-Dehesa Moreno-Cid, J. (2021). Viscothermal effects in a two-dimensional acoustic black hole: A boundary element approach. Physical Review Applied. 15(6):1-14. https://doi.org/10.1103/PhysRevApplied.15.064057S11415

Poisson-like effect for flexural waves in periodically perforated thin plates

[EN] The Poisson-like effect, describing the redirection of waves by 90 degrees, is shown to be feasible for flexural waves propagating in perforated thin plates. It is demonstrated that the lowest order symmetric leaky guided mode (S0 mode) is responsible for the splitting of wave motion in two orthogonal directions. The S0 mode shows a feature of stationary waves containing standing wave modes in one and two orthogonal directions for smaller and larger holes, respectively. The former case is well understood thanks to the phenomenon of Wood's anomaly, which was first observed in optical gratings supposed to be transparent. On the contrary, the strong scattering caused by the larger holes leads to a mixed mode occurring when the incident wave is totally transmitted. The mixed mode easily couples with the incoming waves and, therefore, the Poisson-like effect activated under this mechanism is much stronger. Using the Poisson-like effect, a device is proposed in which about 82% of the incident mechanical energy is redirected to the perpendicular direction. Results obtained with arrays of free holes also apply to inclusions with parameters properly chosen. The findings may provide applications in beam splitting and waveguiding. (C) 2018 Acoustical Society of America.Work supported by the Ministerio de Economia y Competitividad of Spain and the EU Fondo Europeo de Desarrollo Regional under Project No. TEC2014-53088-C3-1-R, and the National Natural Science Foundation of China under Grants Nos. 11432004 and 11421091. P.G. acknowledges a scholarship with No. 201606120070 provided by China Scholarship Council.Gao, P.; Sánchez-Dehesa Moreno-Cid, J.; Wu, L. (2018). Poisson-like effect for flexural waves in periodically perforated thin plates. The Journal of the Acoustical Society of America. 144(2):1053-1058. https://doi.org/10.1121/1.5051648S10531058144

Optimum control of broadband noise by arrays of cylindrical units made of a recycled material

[EN] We report acoustic barriers that are designed to attenuate efficiently broadband noise. The barriers are structures consisting of only three layers of cylindrical units containing rubber crumb, a sound absorbing material obtained from recycling used tires. An optimization algorithm is developed to obtain the material distribution and dimensions of the building units giving the best attenuation properties for traffic noise, which is here chosen as an example in which the design procedure is applied. A good agreement is found between predictions and measurements for a 3 m height barrier that has been characterized in a transmission room. (C) 2012 Elsevier Ltd. All rights reserved.Work supported by the Spanish MICINN under Contracts TEC2010-19751 and CSD2008-00066 (CONSOLIDER program). We acknowledge F. Simon for data acquisition, D. Torrent for useful discussions and L.-W. Cai for the critical reading of manuscript.García Chocano, VM.; Sánchez-Dehesa Moreno-Cid, J. (2013). Optimum control of broadband noise by arrays of cylindrical units made of a recycled material. Applied Acoustics. 74(1):58-62. https://doi.org/10.106/j.apacoust.2012.06.08S586274

Radial Photonic Crystal Shells and Their Application as Resonant and Radiating Elements

Radial photonic crystals (RPCs) are a class of microstructured media that possess very particular electromagnetic features. Their properties are driven by radially dependent permittivity and permeability profiles that are also anisotropic. A two dimensional RPC structure is designed and analyzed in order to assess its principal characteristics. This is done through the study of the dispersion diagram of the periodic multilayered structure and also through the analysis of a finite size device. In the later case, research is performed in view of possible applications of RPCs as resonant devices and also when they are combined with line sources. Finally, a device with reduced complexity is designed and implemented by means of a microstructured resonator array. This device is numerically analyzed and the comparison of two independent models shows very good agreement. Potential use of RPCs as frequency and location sensors is pointed out.Carbonell Olivares, J.; Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2013). Radial Photonic Crystal Shells and Their Application as Resonant and Radiating Elements. IEEE Transactions on Antennas and Propagation. 61(2):755-767. doi:10.1109/TAP.2012.2225015S75576761

Wireless energy transfer between anisotropic metamaterials shells

The behavior of strongly coupled Radial Photonic Crystals shells is investigated as a potential alternative to transfer electromagnetic energy wirelessly. These sub-wavelength resonant microstructures, which are based on anisotropic metamaterials, can produce efficient coupling phenomena due to their high quality factor. A configuration of selected constitutive parameters (permittivity and permeability) is analyzed in terms of its resonant characteristics. The coupling to loss ratio between two coupled resonators is calculated as a function of distance, the maximum (in excess of 300) is obtained when the shells are separated by three times their radius. Under practical conditions an 83% of maximum power transfer has been also estimated.This work was supported by the Spanish Ministry of Economy and Competitiveness under Grants TEC 2010-19751 and Consolider CSD2008-00066. The authors acknowledge Daniel Torrent for useful discussions.Diaz Rubio, A.; Carbonell Olivares, J.; Sánchez-Dehesa Moreno-Cid, J. (2014). Wireless energy transfer between anisotropic metamaterials shells. Annals of Physics. 345:55-62. doi:10.1016/j.aop.2014.03.005S556234

Numerical modeling of double-negative acoustic metamaterials: Should losses be included?

[EN] Viscous and thermal losses of acoustic waves are usually neglected or accounted for as boundary impedance. It is known, however, that acoustic losses become relevant in devices with some dimension in the millimeter range or below. On the other hand, the new class of structures called acoustic metamaterials can be affected by acoustic losses, but in this case the extension of these effects is less known. Acoustic metamaterials are intricate periodic structures where, at frequencies low enough ( corresponding to wavelengths much l arger than the structure period), elementary units interact producing interesting unusual effects. In this paper advanced modeling tools based on the Boundary Element Method (BEM) and the Finite Element Method (FEM) are used to study the effect of losses in an acoustic metamaterial scaled to different sizes. The conclusions are expected to give insight on the practical limitations when using acoustic metamaterialsJ. Sanchez-Dehesa acknowledges the support by the Spanish Ministerio de Economía y Competitividad, and the European Union Fondo Europeo de Desarrollo Regional (FEDER) through Project No. TEC2014-53088-C3-1-RCutanda Henriquez, V.; Andersen, PR.; Sánchez-Dehesa Moreno-Cid, J. (2016). Numerical modeling of double-negative acoustic metamaterials: Should losses be included?. Universidade do Porto. 1-8. http://hdl.handle.net/10251/181075S1

Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells

[EN] The scattering of sound by finite and infinite chains of equally spaced perforated metallic cylindrical shells in an ideal (inviscid) and viscous fluid is theoretically studied using rigorous analytical and numerical approaches. Because of perforations, a chain of thin shells is practically transparent for sound within a wide range of frequencies. It is shown that strong scattering and redirection of sound by 90° may occur only for a discrete set of frequencies (Wood¿s anomalies) where the leaky eigenmodes are excited. The spectrum of eigenmodes consists of antisymmetric and symmetric branches with normal and anomalous dispersion, respectively. The antisymmetric eigenmode turns out to be a deaf mode, since it cannot be excited at normal incidence. However, at slightly oblique incidence, both modes can be resonantly excited at different but close frequencies. The symmetric mode, due to its anomalous dispersion, scatters sound in the ¿wrong¿ direction. This property may find an application for the splitting of the two resonant harmonics of the incoming signal into two beams propagating along the chain in the opposite directions. A chain of perforated cylinders may also be used as a passive antenna that detects the direction to the incoming signal by measuring the frequencies of the waves excited in the chain. Calculations are presented for aluminum shells in viscous air where the effects of anomalous scattering, redirection, and signal splitting are well manifested.A. K. acknowledges support from Programa de Apoyo a la Investigacion y Desarrollo (PAID-02-15) de la Universitat Politecnica de Valencia. A. B., F. C., and J. S.-D. acknowledge the support by the Ministerio de Economia y Competitividad of the Spanish government and the European Union Fondo Europeo de Desarrollo Regional (FEDER) through Project No. TEC2014-53088-C3-1-R. The authors are thankful to Michael R. Haberman for fruitful discussion regarding possible applications of the periodic chain of a perforated shell in the processing of acoustic signals.Bozhko, A.; Sánchez-Dehesa Moreno-Cid, J.; Cervera Moreno, FS.; Krokhin, A. (2017). Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells. Physical Review Applied. 7(6):064034-1-064034-13. doi:10.1103/PhysRevApplied.7.064034S064034-1064034-137

Analysis of flexural wave cloaks

This work presents a comprehensive study of the cloak for bending waves theoretically proposed by Farhat et al. [see Phys. Rev. Lett. 103, 024301 (2009)] and later on experimentally realized by Stenger et al. [see Phys. Rev. Lett. 108, 014301 (2012)]. This study uses a semi-analytical approach, the multilayer scattering method, which is based in the Kirchoff-Love wave equation for flexural waves in thin plates. Our approach was unable to reproduce the predicted behavior of the theoretically proposed cloak. This disagreement is here explained in terms of the simplified wave equation employed in the cloak design, which employed unusual boundary conditions for the cloaking shell. However, our approach reproduces fairly well the measured displacement maps for the fabricated cloak, indicating the validity of our approach. Also, the cloak quality has been here analyzed using the so called averaged visibility and the scattering cross section. The results obtained from both analysis let us to conclude that there is room for further improvements of this type of flexural wave cloak by using better design procedures. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).This work has been supported by the Spanish Ministerio de Economia y Competitividad and the European Union Fondo Europeo para el Desarrollo Regional (FEDER) under Grant with Ref. TEC2014-53088-C3-1-R. We gratefully acknowledge Nicolas Stenger for providing us the parameters listed in Table I.Climente Alarcón, A.; Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2016). Analysis of flexural wave cloaks. AIP Advances. 6(12):121704-1-121705-16. https://doi.org/10.1063/1.4968611S121704-1121705-1661

Single-phase metamaterial plates for broadband vibration suppression at low frequencies

[EN] By studying platonic crystals based on lattices of cavities containing N-beam resonators, we conclude that crystals made of 1-beam resonators easily produce low-frequency omnidirectional bandgaps. Based on this favorable property, hardly obtained for resonant cavities containing a higher number of beams N >= 2, we have designed single-phase metamaterial plates for the suppression of low frequency flexural waves in a broad range of frequencies. These metamaterials are obtained by using resonant cavities containing a multiple number M of identical 1-beam resonators uniformly distributed in the cavity. Square lattices of this type of resonators have been studied by using the impedance matrix approach and the multiple scattering method. This semi-analytical method has been employed to show the existence of complete bandgaps whose width can be optimized by increasing M. For the case M = 4, the largest number of resonators studied here, three complete bandgaps separated by two narrow passbands appear in the band structure. The formation of these complete bandgaps originates from the dynamic interaction between different local resonators as well as their interaction with the propagating waves in the host plate. By using composite structures consisting of platonic crystal slabs with complementary bandgaps, these separated bandgaps easily merge into a broadband wave attenuation region. The normalized width, defined as the percentage of the bandwidth to its central frequency, reaches 95.3%, representing an enhancement of about one order of magnitude compared with the absolute bandwidth obtained for the case of a single 1-beam resonator in the cavity. It is shown that the gaps can be easily tuned to lower frequencies by changing the geometrical parameters, such as the length of the beam, the radius and thickness of the smaller circular plate. Since the metamaterial is made of a single-phase material without attaching heavy masses, the work reported here provides a simple approach to construct low-cost structures with potential applications in aeronautic and astronautic industries for broadband vibration suppression at low frequencies. (C) 2018 Published by Elsevier Ltd.This work was supported by the Ministerio de Economia y Competitividad of the Spanish government and the European Union Fondo Europeo de Desarrollo Regional (FEDER) [Grant No. TEC2014-53088-C3-1-R], and the National Natural Science Foundation of China [Grant Nos. 11432004 and 11421091]. Penglin Gao acknowledges a scholarship provided by China Scholarship Council [Grant No. 201606120070].Gao, P.; Climente Alarcón, A.; Sánchez-Dehesa Moreno-Cid, J.; Wu, L. (2019). Single-phase metamaterial plates for broadband vibration suppression at low frequencies. Journal of Sound and Vibration. 444:108-126. https://doi.org/10.1016/j.jsv.2018.12.022S10812644

Theoretical study of platonic crystals with periodically structured N-beam resonators

[EN] A multiple scattering theory is applied to study the properties of flexural waves propagating in a plate with periodically structured N-beam resonators. Each resonator consists of a circular hole containing an inner disk connected to background plate with N rectangular beams. The Bloch theorem is employed to obtain the band structure of a two-dimensional lattice containing a single resonator per unit cell. Also, a numerical algorithm has been developed to get the transmittance through resonator slabs infinitely long in the direction perpendicular to the incident wave. For the numerical validation, a square lattice of 2-beam resonators has been comprehensively analyzed. Its band structure exhibits several flat bands, indicating the existence of local resonances embedded in the structure. Particularly, the one featured as the fundamental mode of the inner disk opens a bandgap at low frequencies. This mode has been fully described in terms of a simple spring-mass model. As a practical application of the results obtained, a homogenization approach has been employed to design a focusing lens for flexural waves, where the index gradient is obtained by adjusting the orientation of the resonators beams. Numerical experiments performed within the framework of a three-dimensional finite element method have been employed to discuss the accuracy of the models described here. Published by AIP Publishing.This work was supported by the Ministerio de Economia y Competitividad of the Spanish government and the European Union Fondo Europeo de Desarrollo Regional (FEDER) through Project No. TEC2014-53088-C3-1-R, and the National Science Foundation of China under Grant No. 11432004. Penglin Gao acknowledges a scholarship with No. 201606120070 provided by China Scholarship Council.Gao, P.; Climente Alarcón, A.; Sánchez-Dehesa Moreno-Cid, J.; Wu, L. (2018). Theoretical study of platonic crystals with periodically structured N-beam resonators. Journal of Applied Physics. 123(9). https://doi.org/10.1063/1.5009170S123