Phononic crystal diffraction gratings

The present work reports a combined experimental and theoretical study on the acoustic band gaps in a two-dimensional (2D) phononic crystal (PC) consisting of periodic square arrays of stainless-steel cylinders with diameters of 1.0 mm and a lattice constant of 1.5 mm in water. The theoretical band structure of the 2D PC was calculated along the ΓX direction of the first Brillouin zone. The transmission and the reflection coefficients were obtained both experimentally and theoretically along the ΓX direction of the 2D PC. The 2D PC exhibited 5 band gaps at frequencies below 2.0 MHz, with the first Bragg gap being around a frequency of 0.5 MHz. To understand the band gaps in the 2D PC, we calculated the acoustic pressure fields at specific frequencies of interest for normal incidence, and we explained them from the perspective of acoustic diffraction gratings.

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“…From the grating law, the cutoff frequency for the m-th order of diffraction in a host medium can be calculated for normal incidence as [24,25] …”

Section: Resultsmentioning

confidence: 99%

Acoustic band gaps with diffraction gratings in a two-dimensional phononic crystal with a square lattice in water

Lee

Kang

Yoon

2016

Journal of the Korean Physical Society

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“…20, 21 Leroy et al 22,23 considered a layer method for modeling the reflection coefficients from successive thin layers three-dimensional (3D) of bubbles under low frequency limits; their analysis is not applicable here as we only consider two-dimensional (2D) PCs at arbitrary frequencies. Moiseyenko et al 24,25 conducted numerical FE studies that focused on diffraction of the incident wave but without a quantitative independent verification study of the pressure field results. Sanchis et al 26 compared pressure fields using doubly multiple scattering theory versus experiment for an array of 35 aluminum cylinders periodically spaced in air.…”

Section: Introductionmentioning

confidence: 99%

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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“…Additionally, to prevent radiation from truncated computational boundaries from corrupting the results, either a very large homogeneous domain must be employed, or specialized radiation boundary conditions must be developed. 5 In the context of periodic media, the Bloch theorem 16,17 allows one to avoid studying the entire system and to instead consider a single unit cell for computation of the band structure. This theorem enables direct calculation of the dispersion behavior and a set of Bloch waves which describe the wave field within the PC.…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional Bloch wave expansion to determine external scattering from finite phononic crystals

Kulpe

Sabra

Leamy

2015

The Journal of the Acoustical Society of America

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External scattering from a finite phononic crystal (PC) is studied using the Helmholtz-Kirchhoff integral theorem integrated with a Bloch wave expansion (BWE). The BWE technique is used to describe the internal pressure field of a semi-infinite or layered PC subject to an incident monochromatic plane wave. Following the BWE solution, the Helmholtz-Kirchhoff integral is used to determine the external scattered field. For cubic PCs, the scattered results are compared to numerical treatments in both the frequency and time domain. The presented approach is expected to be valid when the PC size is larger than the acoustic wavelength. However, very good agreement in the spatial beam pattern is also documented for both large and small (with respect to the wavelength) PCs. The result of this work is a fully-analytical, efficient, and verified approach for accurately predicting external scattering from finite, three-dimensional PCs.

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Phononic crystal diffraction gratings

Abstract: International audienc

Cited by 24 publications

References 19 publications

Acoustic band gaps with diffraction gratings in a two-dimensional phononic crystal with a square lattice in water

Acoustic band gaps with diffraction gratings in a two-dimensional phononic crystal with a square lattice in water

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

A three-dimensional Bloch wave expansion to determine external scattering from finite phononic crystals

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