Designing 2D Phononic Crystal Slabs with Transmission Gaps for Solid Angle as well as Frequency Variation

Ivansson, Sven

doi:10.1155/2009/317890

Cited by 3 publications

(3 citation statements)

References 18 publications

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“…The computations are typically restricted to in-plane propagation, 15,16 but incidence solid angle variations including mixtures with out-ofplane propagation have also been considered. 17,18 A sound transmission application of interest concerns alternatives to conventional noise barriers at audible frequencies. [19][20][21] The reflection reduction application is studied in the present paper, with the LMS method, and anechoic coatings of different diffraction grating types are compared.…”

Section: In Several Respectsmentioning

confidence: 99%

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Anechoic coatings obtained from two- and three-dimensional monopole resonance diffraction gratings

Ivansson

2012

The Journal of the Acoustical Society of America

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Underwater sound reflections can be reduced in magnitude by a rubber coating including three-dimensional (3-D) cavities forming a doubly periodic diffraction grating. A monopole resonance for sphere-like cavities enhances absorption in the surrounding rubber solid. A corresponding resonance for an infinite cylinder is studied in the present paper. Appearing at a considerably lower frequency than for a sphere with the same radius, it suggests the possibility of much thinner anechoic coatings including cylindrical cavities, with axes in a lateral direction, forming a diffraction grating with a single period. This is effectively a 2-D case, because of invariance in the axial direction. Subsequent coating design computations, using the layer-multiple-scattering method and including cavities of different sizes, show improved reflection reduction with coatings only about one third as thick. Still accounting for multiple scattering among the cavities and capturing the essential physics, the monopole approximation is applied to advance the analytic study of the reflection reduction. An energy decomposition relation is derived and used to quantify the absorption of the incident sound energy by cavities of different sizes. Coatings based on filled inclusions and other resonance effects are briefly considered. Again, the 2-D alternative with cylinders of mixed sizes gives thinner coatings.

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Section: In Several Respectsmentioning

confidence: 99%

“…18 for the regular and outgoing cases, involving the Bessel function J l and the Hankel function H ð1Þ l , respectively. The index l ¼ 0, 61, 6,…, and j is a real number controlling the dependence on y according to the factor expðijyÞ.…”

Section: A the T (Transition) Matrixmentioning

confidence: 99%

Anechoic coatings obtained from two- and three-dimensional monopole resonance diffraction gratings

Ivansson

2012

The Journal of the Acoustical Society of America

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“…Cavity-type scatterers were used already in the Second World War, [1] and have received much attention over the past several decades. [2][3][4][5][6][7][8][9][10][11][12][13] Recently, locally resonant scatterers, [14] which consist of a soft coating layer and a heavy core, have been introduced into the design of anechoic layers and shown efficient low-frequency absorption. [15][16][17][18][19][20] Traditionally, the scatterers in the anechoic layers are ar-ranged in a doubly periodic lattice, however, the anechoic layers with singly periodic lattice have seldom been discussed.…”

Section: Introductionmentioning

confidence: 99%

Acoustic anechoic layers with singly periodic array of scatterers: Computational methods, absorption mechanisms, and optimal design

Yang¹,

Li²,

Zhao³

et al. 2014

Chinese Phys. B

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The acoustic properties of anechoic layers with a singly periodic array of cylindrical scatterers are investigated. A method combined plane wave expansion and finite element analysis is extended for out-of-plane incidence. The reflection characteristics of the anechoic layers with cavities and locally resonant scatterers are discussed. The backing is a steel plate followed by an air half space. Under this approximate zero transmission backing condition, the reflection reduction is induced by the absorption enhancement. The absorption mechanism is explained by the scattering/absorption cross section of the isolated scatterer. Three types of resonant modes which can induce efficient absorption are revealed. Due to the fact that the frequencies of the resonant modes are related to the size of the scatterers, anechoic layers with scatterers of mixed size can broaden the absorption band. A genetic optimization algorithm is adopted to design the anechoic layer with scatterers of mixed size at a desired frequency band from 2 kHz to 10 kHz for normal incidence, and the influence of the incident angle is also discussed.

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Markov-chain Monte Carlo identification of favorable design choices with application to anechoic coatings

Ivansson

2014

The Journal of the Acoustical Society of America

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Global optimization methods can be used to numerically determine optimal design parameters for an object. However, this does not by itself give a good appreciation of other parameter choices that may be almost as good and even preferable from other points of view. In the present paper, Markov-chain Monte Carlo methods are used to go beyond the optimal solution and create an ensemble of object models in parameter space that covers a set of favorable models uniformly. In direct analogy with applications to Bayesian inversion with determination of an unknown posterior probability density, projections of the model ensemble onto parameter axes and planes are used to exhibit parameter sensitivities and dependencies. Design of anechoic rubber coatings, with cylinder cavities having axes in a lateral direction, is considered as a particular application. The anechoic effect is evaluated by the efficient layer-multiple-scattering method, which is extended to handle cylinder scatterers of noncircular cross sections and mixed types. As anticipated by computed scattering and absorption cross sections for an isolated cavity, the favorable coatings have oblate cavity cross-section shapes, which is useful to achieve good low-frequency reflection reduction with a thin coating.

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Designing 2D Phononic Crystal Slabs with Transmission Gaps for Solid Angle as well as Frequency Variation

Cited by 3 publications

References 18 publications

Anechoic coatings obtained from two- and three-dimensional monopole resonance diffraction gratings

Anechoic coatings obtained from two- and three-dimensional monopole resonance diffraction gratings

Acoustic anechoic layers with singly periodic array of scatterers: Computational methods, absorption mechanisms, and optimal design

Markov-chain Monte Carlo identification of favorable design choices with application to anechoic coatings

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