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Article: 3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method
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Title3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method
 
AuthorsZhou, D1
Lo, SH2
Cheung, YK2
 
KeywordsBoundary conditions
Chebyshev approximation
Polynomial approximation
Linear elasticity theories
Vibration spectrums
 
Issue Date2009
 
PublisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/jsvi
 
CitationJournal Of Sound And Vibration, 2009, v. 320 n. 1-2, p. 421-437 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.jsv.2008.08.001
 
AbstractThe three-dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the Chebyshev-Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. The product of Chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the Ritz method. The boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the Chebyshev polynomials provide the robustness for numerical calculation. The present study provides a full vibration spectrum for the thick annular sector plates, which cannot be given by the two-dimensional (2-D) theories such as the Mindlin theory. Comprehensive numerical results with high accuracy are systematically produced, which can be used as benchmark to evaluate other numerical methods. The effect of radius ratio, thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120° to 360° is discussed in detail. The three-dimensional vibration solutions for plates with a re-entrant sector angle (larger than 180°) and shallow helicoidal shells (sector angle larger than 360°) with a small helix angle are presented for the first time. © 2008 Elsevier Ltd. All rights reserved.
 
ISSN0022-460X
2013 Impact Factor: 1.857
 
DOIhttp://dx.doi.org/10.1016/j.jsv.2008.08.001
 
ISI Accession Number IDWOS:000262790500024
 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorZhou, D
 
dc.contributor.authorLo, SH
 
dc.contributor.authorCheung, YK
 
dc.date.accessioned2011-09-23T05:44:55Z
 
dc.date.available2011-09-23T05:44:55Z
 
dc.date.issued2009
 
dc.description.abstractThe three-dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the Chebyshev-Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. The product of Chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the Ritz method. The boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the Chebyshev polynomials provide the robustness for numerical calculation. The present study provides a full vibration spectrum for the thick annular sector plates, which cannot be given by the two-dimensional (2-D) theories such as the Mindlin theory. Comprehensive numerical results with high accuracy are systematically produced, which can be used as benchmark to evaluate other numerical methods. The effect of radius ratio, thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120° to 360° is discussed in detail. The three-dimensional vibration solutions for plates with a re-entrant sector angle (larger than 180°) and shallow helicoidal shells (sector angle larger than 360°) with a small helix angle are presented for the first time. © 2008 Elsevier Ltd. All rights reserved.
 
dc.description.naturelink_to_subscribed_fulltext
 
dc.identifier.citationJournal Of Sound And Vibration, 2009, v. 320 n. 1-2, p. 421-437 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.jsv.2008.08.001
 
dc.identifier.doihttp://dx.doi.org/10.1016/j.jsv.2008.08.001
 
dc.identifier.epage437
 
dc.identifier.hkuros195799
 
dc.identifier.isiWOS:000262790500024
 
dc.identifier.issn0022-460X
2013 Impact Factor: 1.857
 
dc.identifier.issue1-2
 
dc.identifier.openurl
 
dc.identifier.scopuseid_2-s2.0-57349180711
 
dc.identifier.spage421
 
dc.identifier.urihttp://hdl.handle.net/10722/139096
 
dc.identifier.volume320
 
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.subjectBoundary conditions
 
dc.subjectChebyshev approximation
 
dc.subjectPolynomial approximation
 
dc.subjectLinear elasticity theories
 
dc.subjectVibration spectrums
 
dc.title3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method
 
dc.typeArticle
 
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Author Affiliations
  1. Nanjing University of Technology
  2. The University of Hong Kong