Angular Band Gaps in Sonic Crystals: Evanescent Waves and Spatial Complex Dispersion Relation

Romero‐García, Vicente; Picó, Rubén; Cebrecos, Alejandro; Staliūnas, Kęstutis; Sánchez‐Morcillo, Víctor J.

doi:10.1115/1.4023832

Cited by 8 publications

(8 citation statements)

References 57 publications

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“…10,11 In addition, the acoustic band structure of PCs can show angular band gaps that can be used as spatial filters of monochromatic sources. 12,13 These angular band gaps forbid the transmission of waves in some range of directions subsequently narrowing the angular distribution of acoustic beams. In this paper, we exploit both phenomena to achieve an ultra-directional sound source.…”

Section: Introductionmentioning

confidence: 99%

Ultra-directional source of longitudinal acoustic waves based on a two-dimensional solid/solid phononic crystal

Morvan

Tinel

Vasseur

et al. 2014

Journal of Applied Physics

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Phononic crystals (PC) can be used to control the dispersion properties of acoustic waves, which are essential to direct their propagation. We use a PC-based two-dimensional solid/solid composite to demonstrate experimentally and theoretically the spatial filtering of a monochromatic non-directional wave source and its emission in a surrounding water medium as an ultra-directional beam with narrow angular distribution. The phenomenon relies on square-shaped equifrequency contours (EFC) enabling self-collimation of acoustic waves within the phononic crystal. Additionally, the angular width of collimated beams is controlled via the EFC size-shrinking when increasing frequency.

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Section: Introductionmentioning

confidence: 99%

Ultra-directional source of longitudinal acoustic waves based on a two-dimensional solid/solid phononic crystal

Morvan

Tinel

Vasseur

et al. 2014

Journal of Applied Physics

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“…Accordingly, all acoustic energy will be perfectly reflected from the PC. Romero-Garcia et al 39 provided theoretical and experimental evidence of an attenuated field within the PC. They refer to this dispersion behavior as angular bandgaps.…”

Section: B Pc Critical Anglementioning

confidence: 98%

Bloch-wave expansion technique for predicting wave reflection and transmission in two-dimensional phononic crystals

Kulpe

Sabra

Leamy

2014

The Journal of the Acoustical Society of America

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In this paper acoustic wave reflection and transmission are studied at the interface between a phononic crystal (PC) and a homogeneous medium using a Bloch wave expansion technique. A finite element analysis of the PC yields the requisite dispersion relationships and a complete set of Bloch waves, which in turn are employed to expand the transmitted pressure field. A solution for the reflected and transmitted wave fields is then obtained using continuity conditions at the half-space interface. The method introduces a group velocity criterion for Bloch wave selection, which when not enforced, is shown to yield non-physical results. Following development, the approach is applied to example PCs and results are compared to detailed numerical solutions, yielding very good agreement. The approach is also employed to uncover bands of incidence angles whereby perfect acoustic reflection from the PC occurs, even for frequencies outside of stop bands.

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“…Periodic structures or locally resonant systems, also known as metamaterials, have revolutionized the control of waves these last years [1,2]. The main physical properties of these structured media, as for example the opening of band gaps [3,4], the slow wave frequency band [5,6], or the spatial filtering [7], among others, can be directly derived from the complex dispersion relation [8][9][10][11][12]. In addition to dispersive effects, wave attenuation can be caused by factors such as geometric attenuation or intrinsic material loss (e.g., heat or viscous dissipation).…”

Section: Introductionmentioning

confidence: 99%

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

2019

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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.

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Angular Band Gaps in Sonic Crystals: Evanescent Waves and Spatial Complex Dispersion Relation

Abstract: American Society of Mechanical Engineers (ASME) Romero García, V.; Picó Vila, R.; Cebrecos Ruiz, A.; Staliünas, K.; Sánchez Morcillo, VJ. (2013)

Cited by 8 publications

References 57 publications

Ultra-directional source of longitudinal acoustic waves based on a two-dimensional solid/solid phononic crystal

Ultra-directional source of longitudinal acoustic waves based on a two-dimensional solid/solid phononic crystal

Bloch-wave expansion technique for predicting wave reflection and transmission in two-dimensional phononic crystals

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

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