Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
DOI: | 10.1002/zamm.202000197 |
Texto Completo: | http://dx.doi.org/10.1002/zamm.202000197 http://hdl.handle.net/11449/233412 |
Resumo: | The parametric pendulum and others different pendular mechanisms were extensively analyzed in current literature because of the chaotic motions. Recently, practical reasons, like energy harvesting, motivated the study of some pendular systems. The resonance and the chaos may occur in multiple and submultiple frequencies based on the natural frequency of the pendulum. In the present paper, a double pendulum is analyzed with two subharmonic frequencies and in the main resonance zone. The results found demonstrate high similarities of the double pendulum with the parametric pendulum when compared the bifurcation diagrams based on varying the amplitude. The conditions in the numerical simulation include a variation in the viscous friction in the joints and different amplitudes and frequency of excitation. The differential equations used dimensionless parameters representing time, frequency, amplitude, friction, position and velocities. Concerning the results, all tests performed have pointed that the same type of motion takes place in the two pendulums after the transient time have already elapsed. |
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Repositório Institucional da UNESP |
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spelling |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zonechaosdouble pendulumresonance zonesubharmonic frequenciesThe parametric pendulum and others different pendular mechanisms were extensively analyzed in current literature because of the chaotic motions. Recently, practical reasons, like energy harvesting, motivated the study of some pendular systems. The resonance and the chaos may occur in multiple and submultiple frequencies based on the natural frequency of the pendulum. In the present paper, a double pendulum is analyzed with two subharmonic frequencies and in the main resonance zone. The results found demonstrate high similarities of the double pendulum with the parametric pendulum when compared the bifurcation diagrams based on varying the amplitude. The conditions in the numerical simulation include a variation in the viscous friction in the joints and different amplitudes and frequency of excitation. The differential equations used dimensionless parameters representing time, frequency, amplitude, friction, position and velocities. Concerning the results, all tests performed have pointed that the same type of motion takes place in the two pendulums after the transient time have already elapsed.Federal University of MaranhãoUNESP-Universidade Estadual PaulistaFederal University of TechnologyUNESP-Universidade Estadual PaulistaFederal University of MaranhãoUniversidade Estadual Paulista (UNESP)Federal University of TechnologyAvanço, Rafael HenriqueBalthazar, José Manoel [UNESP]Tusset, Ângelo MarceloRibeiro, Mauricio Aparecido2022-05-01T08:44:34Z2022-05-01T08:44:34Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1002/zamm.202000197ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik.1521-40010044-2267http://hdl.handle.net/11449/23341210.1002/zamm.2020001972-s2.0-85112760639Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengZAMM Zeitschrift fur Angewandte Mathematik und Mechanikinfo:eu-repo/semantics/openAccess2022-05-01T08:44:34Zoai:repositorio.unesp.br:11449/233412Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:12:17.546481Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone |
title |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone |
spellingShingle |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone Avanço, Rafael Henrique chaos double pendulum resonance zone subharmonic frequencies Avanço, Rafael Henrique chaos double pendulum resonance zone subharmonic frequencies |
title_short |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone |
title_full |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone |
title_fullStr |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone |
title_full_unstemmed |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone |
title_sort |
Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone |
author |
Avanço, Rafael Henrique |
author_facet |
Avanço, Rafael Henrique Avanço, Rafael Henrique Balthazar, José Manoel [UNESP] Tusset, Ângelo Marcelo Ribeiro, Mauricio Aparecido Balthazar, José Manoel [UNESP] Tusset, Ângelo Marcelo Ribeiro, Mauricio Aparecido |
author_role |
author |
author2 |
Balthazar, José Manoel [UNESP] Tusset, Ângelo Marcelo Ribeiro, Mauricio Aparecido |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Federal University of Maranhão Universidade Estadual Paulista (UNESP) Federal University of Technology |
dc.contributor.author.fl_str_mv |
Avanço, Rafael Henrique Balthazar, José Manoel [UNESP] Tusset, Ângelo Marcelo Ribeiro, Mauricio Aparecido |
dc.subject.por.fl_str_mv |
chaos double pendulum resonance zone subharmonic frequencies |
topic |
chaos double pendulum resonance zone subharmonic frequencies |
description |
The parametric pendulum and others different pendular mechanisms were extensively analyzed in current literature because of the chaotic motions. Recently, practical reasons, like energy harvesting, motivated the study of some pendular systems. The resonance and the chaos may occur in multiple and submultiple frequencies based on the natural frequency of the pendulum. In the present paper, a double pendulum is analyzed with two subharmonic frequencies and in the main resonance zone. The results found demonstrate high similarities of the double pendulum with the parametric pendulum when compared the bifurcation diagrams based on varying the amplitude. The conditions in the numerical simulation include a variation in the viscous friction in the joints and different amplitudes and frequency of excitation. The differential equations used dimensionless parameters representing time, frequency, amplitude, friction, position and velocities. Concerning the results, all tests performed have pointed that the same type of motion takes place in the two pendulums after the transient time have already elapsed. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-01-01 2022-05-01T08:44:34Z 2022-05-01T08:44:34Z |
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/10.1002/zamm.202000197 ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 1521-4001 0044-2267 http://hdl.handle.net/11449/233412 10.1002/zamm.202000197 2-s2.0-85112760639 |
url |
http://dx.doi.org/10.1002/zamm.202000197 http://hdl.handle.net/11449/233412 |
identifier_str_mv |
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 1521-4001 0044-2267 10.1002/zamm.202000197 2-s2.0-85112760639 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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_ |
1822182551908777984 |
dc.identifier.doi.none.fl_str_mv |
10.1002/zamm.202000197 |