Article: Three-dimensional vibration analysis of prisms with isosceles triangular cross-section

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TitleThree-dimensional vibration analysis of prisms with isosceles triangular cross-section
AuthorsZhou, D1
Cheung, YK2
Lo, SH2
Au, FTK2
KeywordsElasticity solution
Prism
Ritz method
Three-dimensional vibration
Triangular cross-section
Issue Date2010
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00419/index.htm
CitationArchive Of Applied Mechanics, 2010, v. 80 n. 6, p. 699-710 [How to Cite?]
DOI: http://dx.doi.org/10.1007/s00419-009-0337-7
AbstractThis paper studies the three-dimensional (3-D) free vibration of uniform prisms with isosceles triangular cross-section, based on the exact, linear and small strain elasticity theory. The actual triangular prismatic domain is first mapped onto a basic cubic domain. Then the Ritz method is applied to derive the eigenfrequency equation from the energy functional of the prism. A set of triplicate Chebyshev polynomial series, multiplied by a boundary function chosen to, a priori, satisfy the geometric boundary conditions of the prism is developed as the admissible functions of each displacement component. The convergence and comparison study demonstrates the high accuracy and numerical robustness of the present method. The effect of length-thickness ratio and apex angle on eigenfrequencies of the prisms is studied in detail and the results are compared with those obtained from the classical one-dimensional theory and the 3-D finite element method. Sets of valuable data known for the first time are reported, which can serve as benchmark values in applying various approximate beam and rod theories. © 2009 Springer-Verlag.
ISSN0939-1533
2011 Impact Factor: 0.95
2011 SCImago Journal Rankings: 0.049
DOIhttp://dx.doi.org/10.1007/s00419-009-0337-7
ReferencesReferences in Scopus
DC Field
Value
dc.contributor.authorZhou, D
dc.contributor.authorCheung, YK
dc.contributor.authorLo, SH
dc.contributor.authorAu, FTK
dc.date.accessioned2010-10-19T04:32:44Z
dc.date.available2010-10-19T04:32:44Z
dc.date.issued2010
dc.description.abstractThis paper studies the three-dimensional (3-D) free vibration of uniform prisms with isosceles triangular cross-section, based on the exact, linear and small strain elasticity theory. The actual triangular prismatic domain is first mapped onto a basic cubic domain. Then the Ritz method is applied to derive the eigenfrequency equation from the energy functional of the prism. A set of triplicate Chebyshev polynomial series, multiplied by a boundary function chosen to, a priori, satisfy the geometric boundary conditions of the prism is developed as the admissible functions of each displacement component. The convergence and comparison study demonstrates the high accuracy and numerical robustness of the present method. The effect of length-thickness ratio and apex angle on eigenfrequencies of the prisms is studied in detail and the results are compared with those obtained from the classical one-dimensional theory and the 3-D finite element method. Sets of valuable data known for the first time are reported, which can serve as benchmark values in applying various approximate beam and rod theories. © 2009 Springer-Verlag.
dc.description.naturepublished_or_final_version
dc.description.otherSpringer Open Choice, 01 Dec 2010
dc.identifier.citationArchive Of Applied Mechanics, 2010, v. 80 n. 6, p. 699-710 [How to Cite?]
DOI: http://dx.doi.org/10.1007/s00419-009-0337-7
dc.identifier.citeulike4935435
dc.identifier.doihttp://dx.doi.org/10.1007/s00419-009-0337-7
dc.identifier.epage710
dc.identifier.hkuros175835
dc.identifier.hkuros195765
dc.identifier.isiWOS:000276489400009
dc.identifier.issn0939-1533
2011 Impact Factor: 0.95
2011 SCImago Journal Rankings: 0.049
dc.identifier.issue6
dc.identifier.openurl
dc.identifier.scopuseid_2-s2.0-77952011371
dc.identifier.spage699
dc.identifier.urihttp://hdl.handle.net/10722/124008
dc.identifier.volume80
dc.languageeng
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00419/index.htm
dc.publisher.placeGermany
dc.relation.ispartofArchive of Applied Mechanics
dc.relation.referencesReferences in Scopus
dc.rightsThe original publication is available at www.springerlink.com
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License
dc.subjectElasticity solution
dc.subjectPrism
dc.subjectRitz method
dc.subjectThree-dimensional vibration
dc.subjectTriangular cross-section
dc.titleThree-dimensional vibration analysis of prisms with isosceles triangular cross-section
dc.typeArticle
Author Affiliations
  1. Nanjing University of Technology
  2. The University of Hong Kong