File Download
 
Links for fulltext
(May Require Subscription)
 
Supplementary

Article: Three-dimensional vibration analysis of toroidal sectors with solid circular cross-sections
  • Basic View
  • Metadata View
  • XML View
TitleThree-dimensional vibration analysis of toroidal sectors with solid circular cross-sections
 
AuthorsZhou, D1
Cheung, YK2
Lo, SH2
 
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
 
CitationJournal Of Applied Mechanics, Transactions Asme, 2010, v. 77 n. 4, p. 1-8 [How to Cite?]
DOI: http://dx.doi.org/10.1115/1.4000906
 
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.
 
ISSN0021-8936
2012 Impact Factor: 1.041
2012 SCImago Journal Rankings: 0.554
 
DOIhttp://dx.doi.org/10.1115/1.4000906
 
ISI Accession Number IDWOS:000276867700002
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.accessioned2011-09-23T05:44:52Z
 
dc.date.available2011-09-23T05:44:52Z
 
dc.date.issued2010
 
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.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationJournal Of Applied Mechanics, Transactions Asme, 2010, v. 77 n. 4, p. 1-8 [How to Cite?]
DOI: http://dx.doi.org/10.1115/1.4000906
 
dc.identifier.doihttp://dx.doi.org/10.1115/1.4000906
 
dc.identifier.epage8
 
dc.identifier.hkuros195762
 
dc.identifier.isiWOS:000276867700002
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.issn0021-8936
2012 Impact Factor: 1.041
2012 SCImago Journal Rankings: 0.554
 
dc.identifier.issue4
 
dc.identifier.scopuseid_2-s2.0-77955290209
 
dc.identifier.spage1
 
dc.identifier.urihttp://hdl.handle.net/10722/139086
 
dc.identifier.volume77
 
dc.languageeng
 
dc.publisherA S M E International. The Journal's web site is located at http://asmedl.aip.org/AppliedMechanics
 
dc.publisher.placeUnited States
 
dc.relation.ispartofJournal of Applied Mechanics, Transactions ASME
 
dc.relation.referencesReferences in Scopus
 
dc.subjectChebyshev polynomial
 
dc.subjectElasticity solution
 
dc.subjectRitz method
 
dc.subjectThree-dimensional vibration
 
dc.subjectToroidal sector
 
dc.titleThree-dimensional vibration analysis of toroidal sectors with solid circular cross-sections
 
dc.typeArticle
 
<?xml encoding="utf-8" version="1.0"?>
<item><contributor.author>Zhou, D</contributor.author>
<contributor.author>Cheung, YK</contributor.author>
<contributor.author>Lo, SH</contributor.author>
<date.accessioned>2011-09-23T05:44:52Z</date.accessioned>
<date.available>2011-09-23T05:44:52Z</date.available>
<date.issued>2010</date.issued>
<identifier.citation>Journal Of Applied Mechanics, Transactions Asme, 2010, v. 77 n. 4, p. 1-8</identifier.citation>
<identifier.issn>0021-8936</identifier.issn>
<identifier.uri>http://hdl.handle.net/10722/139086</identifier.uri>
<description.abstract>This 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,&#952;) with the origin on the cross-sectional centerline of the sector and the circumferential coordinate &#966; 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 &#966; and r coordinates, a set of trigonometric series in &#952; coordinate, and a boundary function in terms of &#966;. 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 &#966;0 on the frequency parameters of the sectors are discussed in detail. The three-dimensional vibration mode shapes are also plotted. &#169; 2010 by ASME.</description.abstract>
<language>eng</language>
<publisher>A S M E International. The Journal&apos;s web site is located at http://asmedl.aip.org/AppliedMechanics</publisher>
<relation.ispartof>Journal of Applied Mechanics, Transactions ASME</relation.ispartof>
<subject>Chebyshev polynomial</subject>
<subject>Elasticity solution</subject>
<subject>Ritz method</subject>
<subject>Three-dimensional vibration</subject>
<subject>Toroidal sector</subject>
<title>Three-dimensional vibration analysis of toroidal sectors with solid circular cross-sections</title>
<type>Article</type>
<description.nature>Link_to_subscribed_fulltext</description.nature>
<identifier.doi>10.1115/1.4000906</identifier.doi>
<identifier.scopus>eid_2-s2.0-77955290209</identifier.scopus>
<identifier.hkuros>195762</identifier.hkuros>
<relation.references>http://www.scopus.com/mlt/select.url?eid=2-s2.0-77955290209&amp;selection=ref&amp;src=s&amp;origin=recordpage</relation.references>
<identifier.volume>77</identifier.volume>
<identifier.issue>4</identifier.issue>
<identifier.spage>1</identifier.spage>
<identifier.epage>8</identifier.epage>
<identifier.isi>WOS:000276867700002</identifier.isi>
<publisher.place>United States</publisher.place>
</item>
Author Affiliations
  1. Nanjing University of Technology
  2. The University of Hong Kong