Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review
Autor(a) principal: | |
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Data de Publicação: | 2012 |
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=S1679-78252012000200003 |
Resumo: | This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies. |
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Latin American journal of solids and structures (Online) |
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Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a reviewNonlinear VibrationNonlinear ResponseAnalytical MethodsParameter Perturbation Method (PPM)Variational Iteration Method(VIM)Homotopy Perturbation Method (HPM)Iteration Perturbation Method (IPM)Energy Balance Method (EBM)Parameter-Expansion Method (PEM)Variational Approach (VA)Improved Amplitude Frequency Formulation (IAFF)Max-Min Approach (MMA)Hamiltonian Approach (HA)Homotopy Analysis Method (HAM)ReviewThis review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.Associação Brasileira de Ciências Mecânicas2012-04-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252012000200003Latin American Journal of Solids and Structures v.9 n.2 2012reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/S1679-78252012000200003info:eu-repo/semantics/openAccessBayat,MahmoudPakar,ImanDomairry,Ganjieng2013-01-17T00:00:00Zoai:scielo:S1679-78252012000200003Revistahttp://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:2013-01-17T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review |
title |
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review |
spellingShingle |
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review Bayat,Mahmoud Nonlinear Vibration Nonlinear Response Analytical Methods Parameter Perturbation Method (PPM) Variational Iteration Method(VIM) Homotopy Perturbation Method (HPM) Iteration Perturbation Method (IPM) Energy Balance Method (EBM) Parameter-Expansion Method (PEM) Variational Approach (VA) Improved Amplitude Frequency Formulation (IAFF) Max-Min Approach (MMA) Hamiltonian Approach (HA) Homotopy Analysis Method (HAM) Review |
title_short |
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review |
title_full |
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review |
title_fullStr |
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review |
title_full_unstemmed |
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review |
title_sort |
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review |
author |
Bayat,Mahmoud |
author_facet |
Bayat,Mahmoud Pakar,Iman Domairry,Ganji |
author_role |
author |
author2 |
Pakar,Iman Domairry,Ganji |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Bayat,Mahmoud Pakar,Iman Domairry,Ganji |
dc.subject.por.fl_str_mv |
Nonlinear Vibration Nonlinear Response Analytical Methods Parameter Perturbation Method (PPM) Variational Iteration Method(VIM) Homotopy Perturbation Method (HPM) Iteration Perturbation Method (IPM) Energy Balance Method (EBM) Parameter-Expansion Method (PEM) Variational Approach (VA) Improved Amplitude Frequency Formulation (IAFF) Max-Min Approach (MMA) Hamiltonian Approach (HA) Homotopy Analysis Method (HAM) Review |
topic |
Nonlinear Vibration Nonlinear Response Analytical Methods Parameter Perturbation Method (PPM) Variational Iteration Method(VIM) Homotopy Perturbation Method (HPM) Iteration Perturbation Method (IPM) Energy Balance Method (EBM) Parameter-Expansion Method (PEM) Variational Approach (VA) Improved Amplitude Frequency Formulation (IAFF) Max-Min Approach (MMA) Hamiltonian Approach (HA) Homotopy Analysis Method (HAM) Review |
description |
This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-04-01 |
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=S1679-78252012000200003 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252012000200003 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1679-78252012000200003 |
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.9 n.2 2012 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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1754302886887555072 |