Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis

Detalhes bibliográficos
Autor(a) principal: Shahlaei-Far,Shahram
Data de Publicação: 2016
Outros Autores: Nabarrete,Airton, Balthazar,José Manoel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Latin American journal of solids and structures (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016001001866
Resumo: Abstract This study analyzes the fourth-order nonlinear free vibration of a Timoshenko beam. We discretize the governing differential equation by Galerkin's procedure and then apply the homotopy analysis method (HAM) to the obtained ordinary differential equation of the generalized coordinate. We derive novel analytical solutions for the nonlinear natural frequency and displacement to investigate the effects of rotary inertia, shear deformation, pre-tensile loads and slenderness ratios on the beam. In comparison to results achieved by perturbation techniques, this study demonstrates that a first-order approximation of HAM leads to highly accurate solutions, valid for a wide range of amplitude vibrations, of a high-order strongly nonlinear problem.
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spelling Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysisstrongly nonlinear vibrationhomotopy analysis methodGalerkin methodTimoshenko beamnonlinear natural frequencyAbstract This study analyzes the fourth-order nonlinear free vibration of a Timoshenko beam. We discretize the governing differential equation by Galerkin's procedure and then apply the homotopy analysis method (HAM) to the obtained ordinary differential equation of the generalized coordinate. We derive novel analytical solutions for the nonlinear natural frequency and displacement to investigate the effects of rotary inertia, shear deformation, pre-tensile loads and slenderness ratios on the beam. In comparison to results achieved by perturbation techniques, this study demonstrates that a first-order approximation of HAM leads to highly accurate solutions, valid for a wide range of amplitude vibrations, of a high-order strongly nonlinear problem.Associação Brasileira de Ciências Mecânicas2016-10-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016001001866Latin American Journal of Solids and Structures v.13 n.10 2016reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/1679-78252766info:eu-repo/semantics/openAccessShahlaei-Far,ShahramNabarrete,AirtonBalthazar,José Manoeleng2016-10-26T00:00:00Zoai:scielo:S1679-78252016001001866Revistahttp://www.scielo.br/scielo.php?script=sci_serial&pid=1679-7825&lng=pt&nrm=isohttps://old.scielo.br/oai/scielo-oai.phpabcm@abcm.org.br||maralves@usp.br1679-78251679-7817opendoar:2016-10-26T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false
dc.title.none.fl_str_mv Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
title Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
spellingShingle Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
Shahlaei-Far,Shahram
strongly nonlinear vibration
homotopy analysis method
Galerkin method
Timoshenko beam
nonlinear natural frequency
title_short Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
title_full Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
title_fullStr Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
title_full_unstemmed Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
title_sort Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
author Shahlaei-Far,Shahram
author_facet Shahlaei-Far,Shahram
Nabarrete,Airton
Balthazar,José Manoel
author_role author
author2 Nabarrete,Airton
Balthazar,José Manoel
author2_role author
author
dc.contributor.author.fl_str_mv Shahlaei-Far,Shahram
Nabarrete,Airton
Balthazar,José Manoel
dc.subject.por.fl_str_mv strongly nonlinear vibration
homotopy analysis method
Galerkin method
Timoshenko beam
nonlinear natural frequency
topic strongly nonlinear vibration
homotopy analysis method
Galerkin method
Timoshenko beam
nonlinear natural frequency
description Abstract This study analyzes the fourth-order nonlinear free vibration of a Timoshenko beam. We discretize the governing differential equation by Galerkin's procedure and then apply the homotopy analysis method (HAM) to the obtained ordinary differential equation of the generalized coordinate. We derive novel analytical solutions for the nonlinear natural frequency and displacement to investigate the effects of rotary inertia, shear deformation, pre-tensile loads and slenderness ratios on the beam. In comparison to results achieved by perturbation techniques, this study demonstrates that a first-order approximation of HAM leads to highly accurate solutions, valid for a wide range of amplitude vibrations, of a high-order strongly nonlinear problem.
publishDate 2016
dc.date.none.fl_str_mv 2016-10-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016001001866
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016001001866
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1679-78252766
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Associação Brasileira de Ciências Mecânicas
publisher.none.fl_str_mv Associação Brasileira de Ciências Mecânicas
dc.source.none.fl_str_mv Latin American Journal of Solids and Structures v.13 n.10 2016
reponame:Latin American journal of solids and structures (Online)
instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)
instacron:ABCM
instname_str Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)
instacron_str ABCM
institution ABCM
reponame_str Latin American journal of solids and structures (Online)
collection Latin American journal of solids and structures (Online)
repository.name.fl_str_mv Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)
repository.mail.fl_str_mv abcm@abcm.org.br||maralves@usp.br
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