Evidences of evanescent Bloch waves in Phononic Crystals

We show both experimentally and theoretically the evanescent behaviour of modes in the Band Gap (BG) of finite Phononic Crystal (PC). Based on experimental and numerical data we obtain the imaginary part of the wave vector in good agreement with the complex band structures obtained by the Extended Plane Wave Expansion (EPWE). The calculated and measured acoustic field of a localized mode out of the point defect inside the PC presents also evanescent behaviour. The correct understanding of evanescent modes is fundamental for designing narrow filters and wave guides based on Phononic Crystals with defects.Comment: 8 pages, 3 figure

Evanescent modes in Sonic Crystals: Complex relation dispersion and supercell approximation

Evanescent modes in complete sonic crystals (SC) and SC with point defects are reported both theoretically and experimentally in this paper. Plane wave expansion (PWE) and, in general, $\omega(k)$ methods have been used to calculate band structures showing gaps that have been interpreted as ranges of frequencies where no real $k$ exists. In this work, we extend PWE to solve the complex $k(\omega)$ problem applied to SC, introducing the supercell approximation for studying one vacancy. Explicit matrix formulation of the equations is given. This $k(\omega)$ method enables the calculation of complex band structures, as well as enabling an analysis of the propagating modes related with real values of the function $k(\omega)$, and the evanescent modes related with imaginary values of $k(\omega)$. This paper shows theoretical results and experimental evidences of the evanescent behavior of modes inside the SC band gap. Experimental data and numerical results using the finite elements method are in very good agreement with the predictions obtained using the $k(\omega)$ method.Comment: 15 pages, 3 figure

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

Compactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operators

[EN] Using compactness properties of bounded subsets of spaces of vector measure integrable functions and a representation theorem for q-convex Banach lattices, we prove a domination theorem for operators between Banach lattices. We generalize in this way several classical factorization results for operators between these spaces, as psumming operators.The authors acknowledge the support of the Generalitat Valenciana, Spain, grant GV04B-371, the Spanish Ministry of Science and Technology, Plan Nacional I+D+I , grant BFM2003-02302; and the support of the Universidad Polit´ecnica de Valencia, under grant 2003-4114 for Interdisciplinary Research Projects.Garcia-Raffi, LM.; Sánchez-Pérez, E. (2005). Compactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operators. Applied General Topology. 6(2):135-142. https://doi.org/10.4995/agt.2005.19521351426

Analytical model to predict the effect of a finite impedance surface on the propagation properties of a 2D Sonic Crystal

The use of Sonic Crystals as environmental noise barriers has certain advantages from the acoustical and the constructive point of view with regard to conventional ones. One aspect do not studied yet is the acoustic interaction between the Sonic Crystals and the ground due to, up to now, this latter is not included in the analytical models used to characterize these Sonic Crystals. We present here an analytical model, based on multiple scattering theory, to study this interaction considering the ground as a finite impedance surface. Using this model we have obtained interesting conclusions that allow to design more effectively noise screens based on Sonic Crystals. The obtained results have been compared with experimental and numerical, finding a good agreement between them

Optimization of sonic crystal attenuation properties by ev-MOGA multiobjective evolutionary algorithm

[EN] This paper shows a promising method for acoustic barrier design using a new acoustic material called Sonic Crystals (SCs). The configuration of these SCs is set as a multiobjective optimization problem which is very difficult to solve with conventional optimization techniques. The paper presents a new parallel implementation of a Multiobjective Evolutionary Algorithm called ev-MOGA (also known as (sic)-MOGA) and its application in a complex design problem. ev-MOGA algorithm has been designed to converge towards a reduced, but well distributed, representation of the Pareto Front (solution of the multiobjective optimization problem). The algorithm is presented in detail and its most important properties are discussed. To reduce the ev-MOGA computational cost when.Partially supported by MEC (Spanish Government) and FEDER funds: projects DPI2005-07835, MAT2006-03097 and Generalitat Valenciana (Spain) projects GV06/026, GV/2007/191Herrero Durá, JM.; Garcia-Nieto, S.; Blasco, X.; Romero García, V.; Sánchez Pérez, JV.; García-Raffi, LM. (2009). Optimization of sonic crystal attenuation properties by ev-MOGA multiobjective evolutionary algorithm. Structural and Multidisciplinary Optimization. 39(2):203-215. https://doi.org/10.1007/s00158-008-0323-7S203215392Alander J (2002) An indexed bibliography of genetic algorithms & pareto and constrainedoptimization. Tech Rep, Dpt of Information Technology, University of VaasaCantú-Paz E (1997) A survey of parallel genetic algorithms. Tech Rep 97003, Illimois Genetic Algorithms LaboratotyCervera F, Sanchis L, Sánchez-Pérez JV, Martínez-Sala R, Rubio C, Meseguer F, López C, Caballero D, Sánchez-Dehesa J (2002) Refractive acoustic devices for airborne sound. 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Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses

Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Romero García, V.; Cebrecos Ruiz, A.; Picó Vila, R.; Sánchez Morcillo, VJ.; García-Raffi, LM.; Sánchez Pérez, JV. (2013). Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses. Applied Physics Letters. 103(26):264106-264106. doi:10.1063/1.4860535 and may be found at http://scitation.aip.org/The symmetry matching between the source and the lens results in fundamental interest for lensing applications. In this work, we have modeled an axisymmetric gradient index (GRIN) lens made of rigid toroidal scatterers embedded in air considering this symmetry matching with radially symmetric sources. The sound amplification obtained in the focal spot of the reported lens (8.24 dB experimentally) shows the efficiency of the axisymmetric lenses with respect to the previous Cartesian acoustic GRIN lenses. The axisymmetric design opens new possibilities in lensing applications in different branches of science and technology.The work was supported by Spanish Ministry of Science and Innovation and European Union FEDER through Project Nos. FIS2011-29734-C02-01 and -02 and PAID 2012/253. V. R. G. is grateful for the support of post-doctoral contracts of the UPV CEI-01-11.Romero García, V.; Cebrecos Ruiz, A.; Picó Vila, R.; Sánchez Morcillo, VJ.; García-Raffi, LM.; Sánchez Pérez, JV. (2013). Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses. Applied Physics Letters. 103(26):264106-264106. https://doi.org/10.1063/1.4860535S26410626410610326John, S. (1987). Strong localization of photons in certain disordered dielectric superlattices. 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Propagating and evanescent properties of duble-point defect in sonic crystals

Complex band structures and multiple scattering theory have been used in this paper to analyze the overlapping of the evanescent waves localized in point defects in sonic crystals (SCs). The extended plane wave expansion (EPWE) with supercell approximation gives the imaginary part of the Bloch vectors that produces the decay of the localized modes inside the periodic system. Double cavities can present a coupling between the evanescent modes localized in the defect, showing a symmetric or antisymmetric mode. When point defects are close, the complex band structures reveal a splitting of the frequencies of the localized modes. Both the real part and the imaginary values of k of the localized modes in the cavities present different values for each localized mode, which gives different properties for each mode. The novel measurements, in very good agreement with analytical data, show experimental evidence of the symmetric and antisymmetric localized modes for a double-point defect in SCs. The investigation of the localization phenomena and the coupling between defects in periodic systems has fundamental importance in both pure and applied physics.This work was supported by MEC (the Spanish Government) and FEDER funds through grants MAT2009-09438 and MTM2009-14483-C02-02.Romero García, V.; Sánchez Pérez, JV.; García-Raffi, LM. (2010). Propagating and evanescent properties of duble-point defect in sonic crystals. New Journal of Physics. 12:1-14. doi:10.1088/1367-2630/12/8/083024S1141