On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://hdl.handle.net/11449/73042 |
Resumo: | This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given. |
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Repositório Institucional da UNESP |
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On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom systemAmplitude frequency responseAnalytical expressionsDuffing oscillatorDynamic behavioursFrequency-response curvesHigher frequenciesLinear oscillatorNonlinear isolatorsResonance frequenciesSingle degree of freedom systemsTwo-degree-of-freedomFrequency responseLinear systemsNatural frequenciesOscillators (mechanical)Nonlinear systemsThis paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.Departamento Do Engenharia Mecãnica Universidade Estadual Paulista, Av. Brasil Centro, 56, 15385-000 Ilha Solteira, Sao PauloDepartment of Mechanical Engineering University of Calabria, Arcavacata di Rende (CS) 87036Departamento Do Engenharia Mecãnica Universidade Estadual Paulista, Av. Brasil Centro, 56, 15385-000 Ilha Solteira, Sao PauloUniversidade Estadual Paulista (Unesp)University of CalabriaBrennan, Michael J. [UNESP]Gatti, Gianluca2014-05-27T11:26:19Z2014-05-27T11:26:19Z2011-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject2783-279018th International Congress on Sound and Vibration 2011, ICSV 2011, v. 4, p. 2783-2790.http://hdl.handle.net/11449/730422-s2.0-84871489490Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPeng18th International Congress on Sound and Vibration 2011, ICSV 2011info:eu-repo/semantics/openAccess2024-07-04T20:06:42Zoai:repositorio.unesp.br:11449/73042Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:46:38.337399Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system |
title |
On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system |
spellingShingle |
On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system Brennan, Michael J. [UNESP] Amplitude frequency response Analytical expressions Duffing oscillator Dynamic behaviours Frequency-response curves Higher frequencies Linear oscillator Nonlinear isolators Resonance frequencies Single degree of freedom systems Two-degree-of-freedom Frequency response Linear systems Natural frequencies Oscillators (mechanical) Nonlinear systems |
title_short |
On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system |
title_full |
On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system |
title_fullStr |
On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system |
title_full_unstemmed |
On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system |
title_sort |
On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system |
author |
Brennan, Michael J. [UNESP] |
author_facet |
Brennan, Michael J. [UNESP] Gatti, Gianluca |
author_role |
author |
author2 |
Gatti, Gianluca |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) University of Calabria |
dc.contributor.author.fl_str_mv |
Brennan, Michael J. [UNESP] Gatti, Gianluca |
dc.subject.por.fl_str_mv |
Amplitude frequency response Analytical expressions Duffing oscillator Dynamic behaviours Frequency-response curves Higher frequencies Linear oscillator Nonlinear isolators Resonance frequencies Single degree of freedom systems Two-degree-of-freedom Frequency response Linear systems Natural frequencies Oscillators (mechanical) Nonlinear systems |
topic |
Amplitude frequency response Analytical expressions Duffing oscillator Dynamic behaviours Frequency-response curves Higher frequencies Linear oscillator Nonlinear isolators Resonance frequencies Single degree of freedom systems Two-degree-of-freedom Frequency response Linear systems Natural frequencies Oscillators (mechanical) Nonlinear systems |
description |
This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-12-01 2014-05-27T11:26:19Z 2014-05-27T11:26:19Z |
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 |
18th International Congress on Sound and Vibration 2011, ICSV 2011, v. 4, p. 2783-2790. http://hdl.handle.net/11449/73042 2-s2.0-84871489490 |
identifier_str_mv |
18th International Congress on Sound and Vibration 2011, ICSV 2011, v. 4, p. 2783-2790. 2-s2.0-84871489490 |
url |
http://hdl.handle.net/11449/73042 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
18th International Congress on Sound and Vibration 2011, ICSV 2011 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
2783-2790 |
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_ |
1808129461050146816 |