File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Accurate analytical perturbation approach for large amplitude vibration of functionally graded beams

TitleAccurate analytical perturbation approach for large amplitude vibration of functionally graded beams
Authors
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
Citation
International Journal Of Non-Linear Mechanics, 2012, v. 47 n. 5, p. 473-480 How to Cite?
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.
Persistent Identifierhttp://hdl.handle.net/10722/157186
ISSN
2014 Impact Factor: 1.977
2014 SCImago Journal Rankings: 1.072
ISI Accession Number ID
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.

References

 

DC FieldValueLanguage
dc.contributor.authorLai, SKen_US
dc.contributor.authorHarrington, Jen_US
dc.contributor.authorXiang, Yen_US
dc.contributor.authorChow, KWen_US
dc.date.accessioned2012-08-08T08:45:43Z-
dc.date.available2012-08-08T08:45:43Z-
dc.date.issued2012en_US
dc.identifier.citationInternational Journal Of Non-Linear Mechanics, 2012, v. 47 n. 5, p. 473-480en_US
dc.identifier.issn0020-7462en_US
dc.identifier.urihttp://hdl.handle.net/10722/157186-
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.en_US
dc.languageengen_US
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/nlmen_US
dc.relation.ispartofInternational Journal of Non-Linear Mechanicsen_US
dc.subjectEuler-Bernoulli Beam Theoryen_US
dc.subjectFunctionally Graded Beamen_US
dc.subjectGeometric Non-Linearityen_US
dc.subjectNon-Linear Differential Equationen_US
dc.subjectPerturbation Approachen_US
dc.titleAccurate analytical perturbation approach for large amplitude vibration of functionally graded beamsen_US
dc.typeArticleen_US
dc.identifier.emailChow, KW:kwchow@hku.hken_US
dc.identifier.authorityChow, KW=rp00112en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.ijnonlinmec.2011.09.019en_US
dc.identifier.scopuseid_2-s2.0-84859743908en_US
dc.identifier.hkuros204446-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84859743908&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume47en_US
dc.identifier.issue5en_US
dc.identifier.spage473en_US
dc.identifier.epage480en_US
dc.identifier.isiWOS:000304848200007-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridLai, SK=35261997800en_US
dc.identifier.scopusauthoridHarrington, J=51863763600en_US
dc.identifier.scopusauthoridXiang, Y=24287121800en_US
dc.identifier.scopusauthoridChow, KW=13605209900en_US
dc.identifier.citeulike9833459-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats