Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , |
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=S1679-78252016000701250 |
Resumo: | Abstract In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load. |
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Latin American journal of solids and structures (Online) |
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Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli BeamsNonlinear vibrationEuler-Bernoulli beamHomotopy Analysis Method (HAM)Two auxiliary parametersDifferential Transform Method (DTM)Abstract In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load.Associação Brasileira de Ciências Mecânicas2016-07-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000701250Latin American Journal of Solids and Structures v.13 n.7 2016reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/1679-78252437info:eu-repo/semantics/openAccessJafari,S.S.Rashidi,M.M.Johnson,S.eng2016-07-25T00:00:00Zoai:scielo:S1679-78252016000701250Revistahttp://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:2016-07-25T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams |
title |
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams |
spellingShingle |
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams Jafari,S.S. Nonlinear vibration Euler-Bernoulli beam Homotopy Analysis Method (HAM) Two auxiliary parameters Differential Transform Method (DTM) |
title_short |
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams |
title_full |
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams |
title_fullStr |
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams |
title_full_unstemmed |
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams |
title_sort |
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams |
author |
Jafari,S.S. |
author_facet |
Jafari,S.S. Rashidi,M.M. Johnson,S. |
author_role |
author |
author2 |
Rashidi,M.M. Johnson,S. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Jafari,S.S. Rashidi,M.M. Johnson,S. |
dc.subject.por.fl_str_mv |
Nonlinear vibration Euler-Bernoulli beam Homotopy Analysis Method (HAM) Two auxiliary parameters Differential Transform Method (DTM) |
topic |
Nonlinear vibration Euler-Bernoulli beam Homotopy Analysis Method (HAM) Two auxiliary parameters Differential Transform Method (DTM) |
description |
Abstract In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-07-01 |
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=S1679-78252016000701250 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000701250 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1679-78252437 |
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.7 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 |
_version_ |
1754302888450981888 |