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dc.contributor.authorSmith, Michael
dc.contributor.authorAbrahams, Ian
dc.date.accessioned2022-06-29T19:43:51Z
dc.date.available2022-06-29T19:43:51Z
dc.date.issued2022-06
dc.date.submitted2022-02-20
dc.identifier.issn1364-5021
dc.identifier.otherrspa20220124
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/338463
dc.description.abstractWe 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.
dc.languageen
dc.publisherThe Royal Society
dc.subjectResearch articles
dc.subjectacoustics
dc.subjectHelmholtz resonator
dc.subjecttwo-dimensional array
dc.subjectmatched asymptotic expansions
dc.subjectmultipole methods
dc.subjectmetamaterial
dc.titleTailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays.
dc.typeArticle
dc.date.updated2022-06-29T19:43:51Z
prism.issueIdentifier2262
prism.publicationNameProc Math Phys Eng Sci
prism.volume478
dc.identifier.doi10.17863/CAM.85876
dcterms.dateAccepted2022-05-16
rioxxterms.versionofrecord10.1098/rspa.2022.0124
rioxxterms.versionAO
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidSmith, Michael [0000-0001-9514-9438]
dc.contributor.orcidAbrahams, Ian [0000-0002-4134-4438]
dc.identifier.eissn1471-2946
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/R014604/1)
cam.issuedOnline2022-06-22


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