Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/978-3-030-77135-5_9 http://hdl.handle.net/11449/222978 |
Resumo: | Dynamical systems containing contact/impact between parts can be modeled as piecewise-smooth reduced-order models. The most common example is freeplay, which can manifest as a loose support, worn hinges, or backlash. Freeplay causes very complex, nonlinear responses in a system that range from isolated resonances to grazing bifurcations to chaos. This can be an issue because classical solution methods, such as direct time integration (e.g., Runge-Kutta) or harmonic balance methods, can fail to accurately detect some of the nonlinear behavior or fail to run altogether. To deal with this limitation, researchers often approximate piecewise freeplay terms in the equations of motion using continuous, fully smooth functions. While this strategy can be convenient, it may not always be appropriate for use. For example, past investigation on freeplay in an aeroelastic control surface showed that, compared to the exact piecewise representation, some approximations are not as effective at capturing freeplay behavior as other ones. Another potential issue is the effectiveness of continuous representations at capturing grazing contacts and grazing-type bifurcations. These can cause the system to transition to high-amplitude responses with frequent contact/impact and be particularly damaging. In this work, a bifurcation study is performed on a model of a forced Duffing oscillator with freeplay nonlinearity. Various representations are used to approximate the freeplay including polynomial, absolute value, and hyperbolic tangent representations. Bifurcation analysis results for each type are compared to results using the exact piecewise-smooth representation computed using MATLAB® Event Location. The effectiveness of each representation is compared and ranked in terms of numerical accuracy, ability to capture multiple response types, ability to predict chaos, and computation time. |
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Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous RepresentationsBifurcation analysisContinuous representationFreeplayNonlinear dynamicsPiecewise-smoothDynamical systems containing contact/impact between parts can be modeled as piecewise-smooth reduced-order models. The most common example is freeplay, which can manifest as a loose support, worn hinges, or backlash. Freeplay causes very complex, nonlinear responses in a system that range from isolated resonances to grazing bifurcations to chaos. This can be an issue because classical solution methods, such as direct time integration (e.g., Runge-Kutta) or harmonic balance methods, can fail to accurately detect some of the nonlinear behavior or fail to run altogether. To deal with this limitation, researchers often approximate piecewise freeplay terms in the equations of motion using continuous, fully smooth functions. While this strategy can be convenient, it may not always be appropriate for use. For example, past investigation on freeplay in an aeroelastic control surface showed that, compared to the exact piecewise representation, some approximations are not as effective at capturing freeplay behavior as other ones. Another potential issue is the effectiveness of continuous representations at capturing grazing contacts and grazing-type bifurcations. These can cause the system to transition to high-amplitude responses with frequent contact/impact and be particularly damaging. In this work, a bifurcation study is performed on a model of a forced Duffing oscillator with freeplay nonlinearity. Various representations are used to approximate the freeplay including polynomial, absolute value, and hyperbolic tangent representations. Bifurcation analysis results for each type are compared to results using the exact piecewise-smooth representation computed using MATLAB® Event Location. The effectiveness of each representation is compared and ranked in terms of numerical accuracy, ability to capture multiple response types, ability to predict chaos, and computation time.Sandia National LaboratoriesMechanical and Aerospace Engineering Department New Mexico State UniversityCampus of São João da Boa Vista São Paulo State UniversitySandia National LaboratoriesCampus of São João da Boa Vista São Paulo State UniversityNew Mexico State UniversityUniversidade Estadual Paulista (UNESP)Sandia National LaboratoriesSaunders, Brian EvanVasconcellos, Rui M. G. [UNESP]Kuether, Robert J.Abdelkefi, Abdessattar2022-04-28T19:47:51Z2022-04-28T19:47:51Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject79-81http://dx.doi.org/10.1007/978-3-030-77135-5_9Conference Proceedings of the Society for Experimental Mechanics Series, p. 79-81.2191-56522191-5644http://hdl.handle.net/11449/22297810.1007/978-3-030-77135-5_92-s2.0-85120525242Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengConference Proceedings of the Society for Experimental Mechanics Seriesinfo:eu-repo/semantics/openAccess2022-04-28T19:47:51Zoai:repositorio.unesp.br:11449/222978Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-06T00:10:12.171886Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations |
title |
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations |
spellingShingle |
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations Saunders, Brian Evan Bifurcation analysis Continuous representation Freeplay Nonlinear dynamics Piecewise-smooth |
title_short |
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations |
title_full |
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations |
title_fullStr |
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations |
title_full_unstemmed |
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations |
title_sort |
Insights on the Bifurcation Behavior of a Freeplay System with Piecewise and Continuous Representations |
author |
Saunders, Brian Evan |
author_facet |
Saunders, Brian Evan Vasconcellos, Rui M. G. [UNESP] Kuether, Robert J. Abdelkefi, Abdessattar |
author_role |
author |
author2 |
Vasconcellos, Rui M. G. [UNESP] Kuether, Robert J. Abdelkefi, Abdessattar |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
New Mexico State University Universidade Estadual Paulista (UNESP) Sandia National Laboratories |
dc.contributor.author.fl_str_mv |
Saunders, Brian Evan Vasconcellos, Rui M. G. [UNESP] Kuether, Robert J. Abdelkefi, Abdessattar |
dc.subject.por.fl_str_mv |
Bifurcation analysis Continuous representation Freeplay Nonlinear dynamics Piecewise-smooth |
topic |
Bifurcation analysis Continuous representation Freeplay Nonlinear dynamics Piecewise-smooth |
description |
Dynamical systems containing contact/impact between parts can be modeled as piecewise-smooth reduced-order models. The most common example is freeplay, which can manifest as a loose support, worn hinges, or backlash. Freeplay causes very complex, nonlinear responses in a system that range from isolated resonances to grazing bifurcations to chaos. This can be an issue because classical solution methods, such as direct time integration (e.g., Runge-Kutta) or harmonic balance methods, can fail to accurately detect some of the nonlinear behavior or fail to run altogether. To deal with this limitation, researchers often approximate piecewise freeplay terms in the equations of motion using continuous, fully smooth functions. While this strategy can be convenient, it may not always be appropriate for use. For example, past investigation on freeplay in an aeroelastic control surface showed that, compared to the exact piecewise representation, some approximations are not as effective at capturing freeplay behavior as other ones. Another potential issue is the effectiveness of continuous representations at capturing grazing contacts and grazing-type bifurcations. These can cause the system to transition to high-amplitude responses with frequent contact/impact and be particularly damaging. In this work, a bifurcation study is performed on a model of a forced Duffing oscillator with freeplay nonlinearity. Various representations are used to approximate the freeplay including polynomial, absolute value, and hyperbolic tangent representations. Bifurcation analysis results for each type are compared to results using the exact piecewise-smooth representation computed using MATLAB® Event Location. The effectiveness of each representation is compared and ranked in terms of numerical accuracy, ability to capture multiple response types, ability to predict chaos, and computation time. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-04-28T19:47:51Z 2022-04-28T19:47:51Z 2022-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/978-3-030-77135-5_9 Conference Proceedings of the Society for Experimental Mechanics Series, p. 79-81. 2191-5652 2191-5644 http://hdl.handle.net/11449/222978 10.1007/978-3-030-77135-5_9 2-s2.0-85120525242 |
url |
http://dx.doi.org/10.1007/978-3-030-77135-5_9 http://hdl.handle.net/11449/222978 |
identifier_str_mv |
Conference Proceedings of the Society for Experimental Mechanics Series, p. 79-81. 2191-5652 2191-5644 10.1007/978-3-030-77135-5_9 2-s2.0-85120525242 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Conference Proceedings of the Society for Experimental Mechanics Series |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
79-81 |
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 |
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1808129591317889024 |