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Article: Accurate analytical perturbation approach for large amplitude vibration of functionally graded beams
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TitleAccurate analytical perturbation approach for large amplitude vibration of functionally graded beams
 
AuthorsLai, SK1
Harrington, J2
Xiang, Y2
Chow, KW1
 
KeywordsEuler-Bernoulli Beam Theory
Functionally Graded Beam
Geometric Non-Linearity
Non-Linear Differential Equation
Perturbation Approach
 
Issue Date2012
 
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/nlm
 
CitationInternational Journal Of Non-Linear Mechanics, 2012, v. 47 n. 5, p. 473-480 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.ijnonlinmec.2011.09.019
 
AbstractThe present work derives the accurate analytical solutions for large amplitude vibration of thin functionally graded beams. In accordance with the Euler-Bernoulli beam theory and the von Kármán type geometric non-linearity, the second-order ordinary differential equation having odd and even non-linearities can be formulated through Hamilton's principle and Galerkin's procedure. This ordinary differential equation governs the non-linear vibration of functionally graded beams with different boundary constraints. Building on the original non-linear equation, two new non-linear equations with odd non-linearity are to be constructed. Employing a generalised Senator-Bapat perturbation technique as an ingenious tool, two newly formulated non-linear equations can be solved analytically. By selecting the appropriate piecewise approximate solutions from such two new non-linear equations, the analytical approximate solutions of the original non-linear problem are established. The present solutions are directly compared to the exact solutions and the available results in the open literature. Besides, some examples are selected to confirm the accuracy and correctness of the current approach. The effects of boundary conditions and vibration amplitudes on the non-linear frequencies are also discussed. © 2011 Elsevier Ltd. All rights reserved.
 
ISSN0020-7462
2013 Impact Factor: 1.463
2013 SCImago Journal Rankings: 0.979
 
DOIhttp://dx.doi.org/10.1016/j.ijnonlinmec.2011.09.019
 
ISI Accession Number IDWOS:000304848200007
Funding AgencyGrant Number
University of Western Sydney20731-80749
Research Grants CouncilHKU7120/08E
University of Hong Kong200911159076
Civionics Research Centre of the University of Western Sydney
Funding Information:

The work described in this paper was supported by the University of Western Sydney through a Research Grant Scheme (Project no. 20731-80749). Partial financial support has been provided by the Research Grants Council contract HKU7120/08E and the University of Hong Kong Seed Funding Program for Basic Research 200911159076. A fellowship offered to the first author for working at the Civionics Research Centre of the University of Western Sydney is also gratefully acknowledged.

 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorLai, SK
 
dc.contributor.authorHarrington, J
 
dc.contributor.authorXiang, Y
 
dc.contributor.authorChow, KW
 
dc.date.accessioned2012-08-08T08:45:43Z
 
dc.date.available2012-08-08T08:45:43Z
 
dc.date.issued2012
 
dc.description.abstractThe present work derives the accurate analytical solutions for large amplitude vibration of thin functionally graded beams. In accordance with the Euler-Bernoulli beam theory and the von Kármán type geometric non-linearity, the second-order ordinary differential equation having odd and even non-linearities can be formulated through Hamilton's principle and Galerkin's procedure. This ordinary differential equation governs the non-linear vibration of functionally graded beams with different boundary constraints. Building on the original non-linear equation, two new non-linear equations with odd non-linearity are to be constructed. Employing a generalised Senator-Bapat perturbation technique as an ingenious tool, two newly formulated non-linear equations can be solved analytically. By selecting the appropriate piecewise approximate solutions from such two new non-linear equations, the analytical approximate solutions of the original non-linear problem are established. The present solutions are directly compared to the exact solutions and the available results in the open literature. Besides, some examples are selected to confirm the accuracy and correctness of the current approach. The effects of boundary conditions and vibration amplitudes on the non-linear frequencies are also discussed. © 2011 Elsevier Ltd. All rights reserved.
 
dc.description.naturelink_to_subscribed_fulltext
 
dc.identifier.citationInternational Journal Of Non-Linear Mechanics, 2012, v. 47 n. 5, p. 473-480 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.ijnonlinmec.2011.09.019
 
dc.identifier.citeulike9833459
 
dc.identifier.doihttp://dx.doi.org/10.1016/j.ijnonlinmec.2011.09.019
 
dc.identifier.epage480
 
dc.identifier.hkuros204446
 
dc.identifier.isiWOS:000304848200007
Funding AgencyGrant Number
University of Western Sydney20731-80749
Research Grants CouncilHKU7120/08E
University of Hong Kong200911159076
Civionics Research Centre of the University of Western Sydney
Funding Information:

The work described in this paper was supported by the University of Western Sydney through a Research Grant Scheme (Project no. 20731-80749). Partial financial support has been provided by the Research Grants Council contract HKU7120/08E and the University of Hong Kong Seed Funding Program for Basic Research 200911159076. A fellowship offered to the first author for working at the Civionics Research Centre of the University of Western Sydney is also gratefully acknowledged.

 
dc.identifier.issn0020-7462
2013 Impact Factor: 1.463
2013 SCImago Journal Rankings: 0.979
 
dc.identifier.issue5
 
dc.identifier.scopuseid_2-s2.0-84859743908
 
dc.identifier.spage473
 
dc.identifier.urihttp://hdl.handle.net/10722/157186
 
dc.identifier.volume47
 
dc.languageeng
 
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/nlm
 
dc.publisher.placeUnited Kingdom
 
dc.relation.ispartofInternational Journal of Non-Linear Mechanics
 
dc.relation.referencesReferences in Scopus
 
dc.subjectEuler-Bernoulli Beam Theory
 
dc.subjectFunctionally Graded Beam
 
dc.subjectGeometric Non-Linearity
 
dc.subjectNon-Linear Differential Equation
 
dc.subjectPerturbation Approach
 
dc.titleAccurate analytical perturbation approach for large amplitude vibration of functionally graded beams
 
dc.typeArticle
 
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Author Affiliations
  1. The University of Hong Kong
  2. University of Western Sydney