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Article: 3-D vibration analysis of circular rings with sectorial cross-sections
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Title3-D vibration analysis of circular rings with sectorial cross-sections
 
AuthorsZhou, D1
Cheung, YK2
Lo, SH2
 
KeywordsChebyshev polynomials
Circular ring
Free vibration characteristic
Linear elasticity theory
Vibration analysis
 
Issue Date2010
 
PublisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/jsvi
 
CitationJournal Of Sound And Vibration, 2010, v. 329 n. 9, p. 1523-1535 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.jsv.2009.11.004
 
AbstractThe free vibration characteristics of circular rings with sectorial cross-section are studied based on the three-dimensional (3-D), small strain, linear elasticity theory. The complete vibration spectrum has been obtained by using the Ritz method. A set of three-dimensional orthogonal coordinates composing of the polar coordinates (r,θ) at the origin of the sectorial cross-section and circumferential coordinate φ{symbol} around the ring is developed to describe the variables in the analysis. Each of the displacement components is taken as a triplicate series: two Chebyshev polynomial series, respectively, about the r and θ coordinates, and a trigonometric series about the φ{symbol} coordinate. Frequency parameters and vibration mode shapes are computed by means of the displacement-based extremum energy principle. Upper bound convergence of the first eight frequency parameters accurate to at least five significant figures is presented. The effect of radius ratio, subtended angle, and initial slope angle on frequency parameters is investigated in detail. All major modes such as flexural modes, thickness-shear modes, stretching modes, and torsional modes, etc. are presented in the paper. The present results may serve as a benchmark reference to validate the accuracy of various approximate theories and other computational techniques for the vibration of circular rings. © 2009 Elsevier Ltd. All rights reserved.
 
ISSN0022-460X
2013 Impact Factor: 1.857
 
DOIhttp://dx.doi.org/10.1016/j.jsv.2009.11.004
 
ISI Accession Number IDWOS:000274758700022
Funding AgencyGrant Number
University of Hong Kong
Funding Information:

The work described in this paper was supported by the CAS membership "Structural vibrations in three-dimensional solids" from The University of Hong Kong.

 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorZhou, D
 
dc.contributor.authorCheung, YK
 
dc.contributor.authorLo, SH
 
dc.date.accessioned2011-09-23T05:44:53Z
 
dc.date.available2011-09-23T05:44:53Z
 
dc.date.issued2010
 
dc.description.abstractThe free vibration characteristics of circular rings with sectorial cross-section are studied based on the three-dimensional (3-D), small strain, linear elasticity theory. The complete vibration spectrum has been obtained by using the Ritz method. A set of three-dimensional orthogonal coordinates composing of the polar coordinates (r,θ) at the origin of the sectorial cross-section and circumferential coordinate φ{symbol} around the ring is developed to describe the variables in the analysis. Each of the displacement components is taken as a triplicate series: two Chebyshev polynomial series, respectively, about the r and θ coordinates, and a trigonometric series about the φ{symbol} coordinate. Frequency parameters and vibration mode shapes are computed by means of the displacement-based extremum energy principle. Upper bound convergence of the first eight frequency parameters accurate to at least five significant figures is presented. The effect of radius ratio, subtended angle, and initial slope angle on frequency parameters is investigated in detail. All major modes such as flexural modes, thickness-shear modes, stretching modes, and torsional modes, etc. are presented in the paper. The present results may serve as a benchmark reference to validate the accuracy of various approximate theories and other computational techniques for the vibration of circular rings. © 2009 Elsevier Ltd. All rights reserved.
 
dc.description.naturelink_to_subscribed_fulltext
 
dc.identifier.citationJournal Of Sound And Vibration, 2010, v. 329 n. 9, p. 1523-1535 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.jsv.2009.11.004
 
dc.identifier.citeulike6212007
 
dc.identifier.doihttp://dx.doi.org/10.1016/j.jsv.2009.11.004
 
dc.identifier.epage1535
 
dc.identifier.hkuros195768
 
dc.identifier.isiWOS:000274758700022
Funding AgencyGrant Number
University of Hong Kong
Funding Information:

The work described in this paper was supported by the CAS membership "Structural vibrations in three-dimensional solids" from The University of Hong Kong.

 
dc.identifier.issn0022-460X
2013 Impact Factor: 1.857
 
dc.identifier.issue9
 
dc.identifier.scopuseid_2-s2.0-74149084857
 
dc.identifier.spage1523
 
dc.identifier.urihttp://hdl.handle.net/10722/139089
 
dc.identifier.volume329
 
dc.languageeng
 
dc.publisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/jsvi
 
dc.publisher.placeUnited Kingdom
 
dc.relation.ispartofJournal of Sound and Vibration
 
dc.relation.referencesReferences in Scopus
 
dc.subjectChebyshev polynomials
 
dc.subjectCircular ring
 
dc.subjectFree vibration characteristic
 
dc.subjectLinear elasticity theory
 
dc.subjectVibration analysis
 
dc.title3-D vibration analysis of circular rings with sectorial cross-sections
 
dc.typeArticle
 
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Author Affiliations
  1. Nanjing University of Technology
  2. The University of Hong Kong