Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
DOI: | 10.1007/s11012-015-0310-1 |
Texto Completo: | http://dx.doi.org/10.1007/s11012-015-0310-1 http://hdl.handle.net/11449/172154 |
Resumo: | The nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crank-shaft-slider mechanism. The novelty is the obtainment and analysis of a mathematical model for the pendulum dynamics, under an excitation of a crank-slider, which is based on an extension of the mathematical model of the classical parametric pendulums. Through the modeling, it was verified that the nonlinear dynamics of the pendulum, excited by the crank-shaft-slider mechanism approaches to that of harmonic excitation, when one considered the length of the shaft is sufficient larger than the radius of the crank. The nonlinear dynamic analyses focused on observation of different kinds of motion for different values of dimensionless parameters of the adopted mathematical model. These parameters, includes the frequency of excitation, the amplitude and the geometry of the crank-shaft-slider mechanism. The adopted method of analyses used tools, such as, Lyapunov exponents, parameter space plots, basins of attractions, bifurcation diagrams, phase portraits, time histories and Poincaré sections. The kinds of motion include results on fixed point, oscillations, rotations, oscillations–rotations and chaotic motions. |
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Repositório Institucional da UNESP |
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Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanismChaosCrank-shaft-sliderParametricPendulumThe nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crank-shaft-slider mechanism. The novelty is the obtainment and analysis of a mathematical model for the pendulum dynamics, under an excitation of a crank-slider, which is based on an extension of the mathematical model of the classical parametric pendulums. Through the modeling, it was verified that the nonlinear dynamics of the pendulum, excited by the crank-shaft-slider mechanism approaches to that of harmonic excitation, when one considered the length of the shaft is sufficient larger than the radius of the crank. The nonlinear dynamic analyses focused on observation of different kinds of motion for different values of dimensionless parameters of the adopted mathematical model. These parameters, includes the frequency of excitation, the amplitude and the geometry of the crank-shaft-slider mechanism. The adopted method of analyses used tools, such as, Lyapunov exponents, parameter space plots, basins of attractions, bifurcation diagrams, phase portraits, time histories and Poincaré sections. The kinds of motion include results on fixed point, oscillations, rotations, oscillations–rotations and chaotic motions.Department of Mechanical Engineering University of São Paulo, Av. Trabalhador São-Carlense, nº 400Federal University of ABC, Santa Adélia Street, nº 166Department of Mechanical Engineering at Technological Institute of Aeronautics, Pça. Mal. Eduardo Gomes, nº 50UNESP: Sorocaba Control and Automation Engineering, Av. Três de MarçoDepartment of Mathematics Federal University of Technology – ParanáUNESP: Sorocaba Control and Automation Engineering, Av. Três de MarçoUniversidade de São Paulo (USP)Federal University of ABCUniversidade Estadual Paulista (Unesp)Federal University of Technology – ParanáAvanço, Rafael HenriqueNavarro, Hélio AparecidoBrasil, Reyolando M. L. R. F.Balthazar, José ManoelBueno, Átila Madureira [UNESP]Tusset, Angelo Marcelo2018-12-11T16:58:57Z2018-12-11T16:58:57Z2016-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1301-1320application/pdfhttp://dx.doi.org/10.1007/s11012-015-0310-1Meccanica, v. 51, n. 6, p. 1301-1320, 2016.1572-96480025-6455http://hdl.handle.net/11449/17215410.1007/s11012-015-0310-12-s2.0-849452747992-s2.0-84945274799.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMeccanica0,8140,814info:eu-repo/semantics/openAccess2023-11-18T06:15:42Zoai:repositorio.unesp.br:11449/172154Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:04:48.880986Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism |
title |
Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism |
spellingShingle |
Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism Avanço, Rafael Henrique Chaos Crank-shaft-slider Parametric Pendulum Avanço, Rafael Henrique Chaos Crank-shaft-slider Parametric Pendulum |
title_short |
Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism |
title_full |
Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism |
title_fullStr |
Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism |
title_full_unstemmed |
Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism |
title_sort |
Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism |
author |
Avanço, Rafael Henrique |
author_facet |
Avanço, Rafael Henrique Avanço, Rafael Henrique Navarro, Hélio Aparecido Brasil, Reyolando M. L. R. F. Balthazar, José Manoel Bueno, Átila Madureira [UNESP] Tusset, Angelo Marcelo Navarro, Hélio Aparecido Brasil, Reyolando M. L. R. F. Balthazar, José Manoel Bueno, Átila Madureira [UNESP] Tusset, Angelo Marcelo |
author_role |
author |
author2 |
Navarro, Hélio Aparecido Brasil, Reyolando M. L. R. F. Balthazar, José Manoel Bueno, Átila Madureira [UNESP] Tusset, Angelo Marcelo |
author2_role |
author author author author author |
dc.contributor.none.fl_str_mv |
Universidade de São Paulo (USP) Federal University of ABC Universidade Estadual Paulista (Unesp) Federal University of Technology – Paraná |
dc.contributor.author.fl_str_mv |
Avanço, Rafael Henrique Navarro, Hélio Aparecido Brasil, Reyolando M. L. R. F. Balthazar, José Manoel Bueno, Átila Madureira [UNESP] Tusset, Angelo Marcelo |
dc.subject.por.fl_str_mv |
Chaos Crank-shaft-slider Parametric Pendulum |
topic |
Chaos Crank-shaft-slider Parametric Pendulum |
description |
The nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crank-shaft-slider mechanism. The novelty is the obtainment and analysis of a mathematical model for the pendulum dynamics, under an excitation of a crank-slider, which is based on an extension of the mathematical model of the classical parametric pendulums. Through the modeling, it was verified that the nonlinear dynamics of the pendulum, excited by the crank-shaft-slider mechanism approaches to that of harmonic excitation, when one considered the length of the shaft is sufficient larger than the radius of the crank. The nonlinear dynamic analyses focused on observation of different kinds of motion for different values of dimensionless parameters of the adopted mathematical model. These parameters, includes the frequency of excitation, the amplitude and the geometry of the crank-shaft-slider mechanism. The adopted method of analyses used tools, such as, Lyapunov exponents, parameter space plots, basins of attractions, bifurcation diagrams, phase portraits, time histories and Poincaré sections. The kinds of motion include results on fixed point, oscillations, rotations, oscillations–rotations and chaotic motions. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-06-01 2018-12-11T16:58:57Z 2018-12-11T16:58:57Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s11012-015-0310-1 Meccanica, v. 51, n. 6, p. 1301-1320, 2016. 1572-9648 0025-6455 http://hdl.handle.net/11449/172154 10.1007/s11012-015-0310-1 2-s2.0-84945274799 2-s2.0-84945274799.pdf |
url |
http://dx.doi.org/10.1007/s11012-015-0310-1 http://hdl.handle.net/11449/172154 |
identifier_str_mv |
Meccanica, v. 51, n. 6, p. 1301-1320, 2016. 1572-9648 0025-6455 10.1007/s11012-015-0310-1 2-s2.0-84945274799 2-s2.0-84945274799.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Meccanica 0,814 0,814 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1301-1320 application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1822230056387215360 |
dc.identifier.doi.none.fl_str_mv |
10.1007/s11012-015-0310-1 |