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Article: Three-dimensional vibration analysis of toroidal sectors with solid circular cross-sections

TitleThree-dimensional vibration analysis of toroidal sectors with solid circular cross-sections
Authors
KeywordsChebyshev polynomial
Elasticity solution
Ritz method
Three-dimensional vibration
Toroidal sector
Issue Date2010
PublisherA S M E International. The Journal's web site is located at http://asmedl.aip.org/AppliedMechanics
Citation
Journal Of Applied Mechanics, Transactions Asme, 2010, v. 77 n. 4, p. 1-8 How to Cite?
AbstractThis paper studies the free vibration of circular toroidal sectors with circular crosssections based on the three-dimensional small-strain, linear elasticity theory. A set of orthogonal coordinates, composing the polar coordinate (r,θ) with the origin on the cross-sectional centerline of the sector and the circumferential coordinate φ with the origin at the curvature center of the centerline, is developed to describe the displacements, strains, and stresses in the sector. Each of the displacement components is taken as a product of four functions: a set of Chebyshev polynomials in φ and r coordinates, a set of trigonometric series in θ coordinate, and a boundary function in terms of φ. Frequency parameters and mode shapes have been obtained via a displacement-based extremum energy principle. The upper bound convergence of the first eight frequency parameters accurate up to five figures has been achieved. The present results agree with those from the finite element solutions. The effect of the ratio of curvature radius R to the cross-sectional radius a and the subtended angle φ0 on the frequency parameters of the sectors are discussed in detail. The three-dimensional vibration mode shapes are also plotted. © 2010 by ASME.
Persistent Identifierhttp://hdl.handle.net/10722/139086
ISSN
2014 Impact Factor: 1.370
2014 SCImago Journal Rankings: 0.496
ISI Accession Number ID
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.

References

 

DC FieldValueLanguage
dc.contributor.authorZhou, Den_HK
dc.contributor.authorCheung, YKen_HK
dc.contributor.authorLo, SHen_HK
dc.date.accessioned2011-09-23T05:44:52Z-
dc.date.available2011-09-23T05:44:52Z-
dc.date.issued2010en_HK
dc.identifier.citationJournal Of Applied Mechanics, Transactions Asme, 2010, v. 77 n. 4, p. 1-8en_HK
dc.identifier.issn0021-8936en_HK
dc.identifier.urihttp://hdl.handle.net/10722/139086-
dc.description.abstractThis paper studies the free vibration of circular toroidal sectors with circular crosssections based on the three-dimensional small-strain, linear elasticity theory. A set of orthogonal coordinates, composing the polar coordinate (r,θ) with the origin on the cross-sectional centerline of the sector and the circumferential coordinate φ with the origin at the curvature center of the centerline, is developed to describe the displacements, strains, and stresses in the sector. Each of the displacement components is taken as a product of four functions: a set of Chebyshev polynomials in φ and r coordinates, a set of trigonometric series in θ coordinate, and a boundary function in terms of φ. Frequency parameters and mode shapes have been obtained via a displacement-based extremum energy principle. The upper bound convergence of the first eight frequency parameters accurate up to five figures has been achieved. The present results agree with those from the finite element solutions. The effect of the ratio of curvature radius R to the cross-sectional radius a and the subtended angle φ0 on the frequency parameters of the sectors are discussed in detail. The three-dimensional vibration mode shapes are also plotted. © 2010 by ASME.en_HK
dc.languageengen_US
dc.publisherA S M E International. The Journal's web site is located at http://asmedl.aip.org/AppliedMechanicsen_HK
dc.relation.ispartofJournal of Applied Mechanics, Transactions ASMEen_HK
dc.subjectChebyshev polynomialen_HK
dc.subjectElasticity solutionen_HK
dc.subjectRitz methoden_HK
dc.subjectThree-dimensional vibrationen_HK
dc.subjectToroidal sectoren_HK
dc.titleThree-dimensional vibration analysis of toroidal sectors with solid circular cross-sectionsen_HK
dc.typeArticleen_HK
dc.identifier.emailCheung, YK:hreccyk@hkucc.hku.hken_HK
dc.identifier.emailLo, SH:hreclsh@hkucc.hku.hken_HK
dc.identifier.authorityCheung, YK=rp00104en_HK
dc.identifier.authorityLo, SH=rp00223en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1115/1.4000906en_HK
dc.identifier.scopuseid_2-s2.0-77955290209en_HK
dc.identifier.hkuros195762en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77955290209&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume77en_HK
dc.identifier.issue4en_HK
dc.identifier.spage1en_HK
dc.identifier.epage8en_HK
dc.identifier.isiWOS:000276867700002-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridZhou, D=7403395115en_HK
dc.identifier.scopusauthoridCheung, YK=7202111065en_HK
dc.identifier.scopusauthoridLo, SH=7401542444en_HK

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