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Open AccessFeature PaperArticle

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

1
Instituto de Instrumentación para Imagen Molecular, CSIC—Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
2
Laboratoire d’Acoustique de l’Université du Mans—CNRS UMR 6613, Av. Olivier Messiaen, 72085 Le Mans, France
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(3), 478; https://doi.org/10.3390/app9030478
Received: 29 December 2018 / Revised: 22 January 2019 / Accepted: 22 January 2019 / Published: 30 January 2019
(This article belongs to the Special Issue Acoustic Metamaterials)
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. View Full-Text
Keywords: complex dispersion relation; acoustic metamaterials; periodic media complex dispersion relation; acoustic metamaterials; periodic media
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MDPI and ACS Style

Cebrecos, A.; Romero-García, V.; Groby, J.P. Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size. Appl. Sci. 2019, 9, 478. https://doi.org/10.3390/app9030478

AMA Style

Cebrecos A, Romero-García V, Groby JP. Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size. Applied Sciences. 2019; 9(3):478. https://doi.org/10.3390/app9030478

Chicago/Turabian Style

Cebrecos, Alejandro; Romero-García, Vicente; Groby, Jean P. 2019. "Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size" Appl. Sci. 9, no. 3: 478. https://doi.org/10.3390/app9030478

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