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Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays.

Published version
Peer-reviewed

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Abstract

We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining existing multipole methods for arrays of ideal cylinders with the method of matched asymptotic expansions. We construct asymptotically close representations for the dispersion equations of the first band surface, correcting and extending an established lowest-order (isotropic) result in the literature for thin-walled resonator arrays. The descriptions we obtain for the first band are accurate over a relatively broad frequency and Bloch vector range and not simply in the long-wavelength and low-frequency regime, as is the case in many classical treatments. Crucially, we are able to capture features of the first band, such as low-frequency anisotropy, over a broad range of filling fractions, wall thicknesses and aperture angles. In addition to describing the first band we use our formulation to compute the first band gap for both thin- and thick-walled resonators, and find that thicker resonator walls correspond to both a narrowing of the first band gap and an increase in the central band gap frequency.

Description

Keywords

Research articles, acoustics, Helmholtz resonator, two-dimensional array, matched asymptotic expansions, multipole methods, metamaterial

Journal Title

Proc Math Phys Eng Sci

Conference Name

Journal ISSN

1364-5021
1471-2946

Volume Title

478

Publisher

The Royal Society
Sponsorship
Engineering and Physical Sciences Research Council (EP/R014604/1)