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

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TitleThree-dimensional vibration analysis of a torus with circular cross section
AuthorsZhou, D1
Au, FTK2
Lo, SH2
Cheung, YK2
KeywordsPhysics - sound
Issue Date2002
PublisherAcoustical Society of America. The Journal's web site is located at http://asa.aip.org/jasa.html
CitationJournal Of The Acoustical Society Of America, 2002, v. 112 n. 6, p. 2831-2839 [How to Cite?]
DOI: http://dx.doi.org/10.1121/1.1509429
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.
ISSN0001-4966
2011 Impact Factor: 1.55
2011 SCImago Journal Rankings: 0.075
DOIhttp://dx.doi.org/10.1121/1.1509429
ISI Accession Number IDWOS:000179824900032
ReferencesReferences in Scopus
DC Field
Value
dc.contributor.authorZhou, D
dc.contributor.authorAu, FTK
dc.contributor.authorLo, SH
dc.contributor.authorCheung, YK
dc.date.accessioned2007-03-23T04:28:49Z
dc.date.available2007-03-23T04:28:49Z
dc.date.issued2002
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.
dc.description.naturepublished_or_final_version
dc.format.extent188978 bytes
dc.format.extent25088 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/msword
dc.identifier.citationJournal Of The Acoustical Society Of America, 2002, v. 112 n. 6, p. 2831-2839 [How to Cite?]
DOI: http://dx.doi.org/10.1121/1.1509429
dc.identifier.citeulike919473
dc.identifier.doihttp://dx.doi.org/10.1121/1.1509429
dc.identifier.epage2839
dc.identifier.hkuros76154
dc.identifier.isiWOS:000179824900032
dc.identifier.issn0001-4966
2011 Impact Factor: 1.55
2011 SCImago Journal Rankings: 0.075
dc.identifier.issue6
dc.identifier.openurl
dc.identifier.pmid12509004
dc.identifier.scopuseid_2-s2.0-0038590393
dc.identifier.spage2831
dc.identifier.urihttp://hdl.handle.net/10722/42648
dc.identifier.volume112
dc.languageeng
dc.publisherAcoustical Society of America. The Journal's web site is located at http://asa.aip.org/jasa.html
dc.publisher.placeUnited States
dc.relation.ispartofJournal of the Acoustical Society of America
dc.relation.referencesReferences in Scopus
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License
dc.subjectPhysics - sound
dc.titleThree-dimensional vibration analysis of a torus with circular cross section
dc.typeArticle
Author Affiliations
  1. Nanjing University of Information Science and Technology
  2. The University of Hong Kong