Show simple item record

dc.contributor.authorSmith, Michael
dc.contributor.authorAbrahams, Ian
dc.date.accessioned2022-06-29T19:44:52Z
dc.date.available2022-06-29T19:44:52Z
dc.date.issued2022-06
dc.date.submitted2022-02-20
dc.identifier.issn1364-5021
dc.identifier.otherrspa20220125
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/338491
dc.description.abstractWe present a solution method which combines the technique of matched asymptotic expansions with the method of multipole expansions to determine the band structure of cylindrical Helmholtz resonator arrays in two dimensions. The resonator geometry is considered in the limit as the wall thickness becomes very large compared with the aperture width (the extremely thick-walled limit). In this regime, the existing treatment in Part I (Smith & Abrahams, 2022 Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays), with updated parameters, is found to return spurious spectral behaviour. We derive a regularized system which overcomes this issue and also derive compact asymptotic descriptions for the low-frequency dispersion equation in this setting. We find that the matched-asymptotic system is able to recover the first few bands over the entire Brillouin zone with ease, when suitably truncated. A homogenization treatment is outlined for describing the effective bulk modulus and effective density tensor of the resonator array for all wall thicknesses. We demonstrate that extremely thick-walled resonators are able to achieve exceptionally low Helmholtz resonant frequencies, and present closed-form expressions for determining these explicitly. We anticipate that the analytical expressions and the formulation outlined here may prove useful in designing metamaterials for industrial and other applications.
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 II. Extremely thick-walled Helmholtz resonator arrays.
dc.typeArticle
dc.date.updated2022-06-29T19:44:52Z
prism.issueIdentifier2262
prism.publicationNameProc Math Phys Eng Sci
prism.volume478
dc.identifier.doi10.17863/CAM.85904
dcterms.dateAccepted2022-05-16
rioxxterms.versionofrecord10.1098/rspa.2022.0125
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


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record