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Article: Three-dimensional vibration analysis of a torus with circular cross section

TitleThree-dimensional vibration analysis of a torus with circular cross section
Authors
KeywordsPhysics - sound
Issue Date2002
PublisherAcoustical Society of America. The Journal's web site is located at http://asa.aip.org/jasa.html
Citation
Journal Of The Acoustical Society Of America, 2002, v. 112 n. 6, p. 2831-2839 How to Cite?
AbstractThe free vibration characteristics of a torus with a circular cross section are studied by using the three-dimensional, small-strain, elasticity theory. A set of three-dimensional orthogonal coordinates system, comprising the polar coordinate (r, θ) at each circular cross section and the circumferential coordinate φ around the ring, is developed. Each of the displacement components ur, vτ, and wφ in the r, θ, and φ directions, respectively, is taken as a product of the Chebyshev polynomials in the r direction and the trigonometric functions in the θ and φ directions. Eigenfrequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions. The eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross-sectional radius are investigated in detail. Very accurate eigenfrequencies and deformed mode shapes of the three-dimensional vibration are presented. All major modes such as flexural thickness-shear modes, in-plane stretching modes, and torsional modes are included in the analysis. The results may serve as a benchmark reference for validating other computational techniques for the problem. © 2002 Acoustical Society of America.
Persistent Identifierhttp://hdl.handle.net/10722/42648
ISSN
2015 Impact Factor: 1.572
2015 SCImago Journal Rankings: 0.938
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorZhou, Den_HK
dc.contributor.authorAu, FTKen_HK
dc.contributor.authorLo, SHen_HK
dc.contributor.authorCheung, YKen_HK
dc.date.accessioned2007-03-23T04:28:49Z-
dc.date.available2007-03-23T04:28:49Z-
dc.date.issued2002en_HK
dc.identifier.citationJournal Of The Acoustical Society Of America, 2002, v. 112 n. 6, p. 2831-2839en_HK
dc.identifier.issn0001-4966en_HK
dc.identifier.urihttp://hdl.handle.net/10722/42648-
dc.description.abstractThe free vibration characteristics of a torus with a circular cross section are studied by using the three-dimensional, small-strain, elasticity theory. A set of three-dimensional orthogonal coordinates system, comprising the polar coordinate (r, θ) at each circular cross section and the circumferential coordinate φ around the ring, is developed. Each of the displacement components ur, vτ, and wφ in the r, θ, and φ directions, respectively, is taken as a product of the Chebyshev polynomials in the r direction and the trigonometric functions in the θ and φ directions. Eigenfrequencies and vibration mode shapes have been obtained via a three-dimensional displacement-based extremum energy principle. Upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions. The eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross-sectional radius are investigated in detail. Very accurate eigenfrequencies and deformed mode shapes of the three-dimensional vibration are presented. All major modes such as flexural thickness-shear modes, in-plane stretching modes, and torsional modes are included in the analysis. The results may serve as a benchmark reference for validating other computational techniques for the problem. © 2002 Acoustical Society of America.en_HK
dc.format.extent188978 bytes-
dc.format.extent25088 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/msword-
dc.languageengen_HK
dc.publisherAcoustical Society of America. The Journal's web site is located at http://asa.aip.org/jasa.htmlen_HK
dc.relation.ispartofJournal of the Acoustical Society of Americaen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectPhysics - sounden_HK
dc.titleThree-dimensional vibration analysis of a torus with circular cross sectionen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0001-4966&volume=112&issue=6&spage=2831&epage=2839&date=2002&atitle=Three-dimensional+vibration+analysis+of+a+torus+with+circular+cross+sectionen_HK
dc.identifier.emailAu, FTK:francis.au@hku.hken_HK
dc.identifier.emailLo, SH:hreclsh@hkucc.hku.hken_HK
dc.identifier.emailCheung, YK:hreccyk@hkucc.hku.hken_HK
dc.identifier.authorityAu, FTK=rp00083en_HK
dc.identifier.authorityLo, SH=rp00223en_HK
dc.identifier.authorityCheung, YK=rp00104en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1121/1.1509429en_HK
dc.identifier.pmid12509004-
dc.identifier.scopuseid_2-s2.0-0038590393en_HK
dc.identifier.hkuros76154-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0038590393&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume112en_HK
dc.identifier.issue6en_HK
dc.identifier.spage2831en_HK
dc.identifier.epage2839en_HK
dc.identifier.isiWOS:000179824900032-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridZhou, D=7403395115en_HK
dc.identifier.scopusauthoridAu, FTK=7005204072en_HK
dc.identifier.scopusauthoridLo, SH=7401542444en_HK
dc.identifier.scopusauthoridCheung, YK=7202111065en_HK
dc.identifier.citeulike919473-

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