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
2011 Impact Factor: 1.588
2011 SCImago Journal Rankings: 0.071
DOIhttp://dx.doi.org/10.1016/j.jsv.2008.08.001
ISI Accession Number IDWOS:000262790500024
ReferencesReferences in Scopus
DC Field
Value
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
2011 Impact Factor: 1.588
2011 SCImago Journal Rankings: 0.071
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
Author Affiliations
  1. Nanjing University of Technology
  2. The University of Hong Kong