Applied nonlinear dynamics of non-smooth mechanical systems

Detalhes bibliográficos
Autor(a) principal: Wiercigroch,Marian
Data de Publicação: 2006
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782006000400018
Resumo: This paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspaceomega. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied. Firstly the vibro-impact system in a form of moling device was modelled and analysed to understand how the progression rates can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces (no contact, contact with progression and contact without progression). In the second application frictional chatter occurring during metal cutting has been examined via numerical simulation method. The analysis has shown that the bifurcation analysis can be very useful to make an appropriate choice of the system parameters to avoid chatter. The last problem comes from rotordynamics, where nonlinear interaction between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation.
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spelling Applied nonlinear dynamics of non-smooth mechanical systemsNonlinear dynamicsnon-smooth systemsmechanical vibrationsThis paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspaceomega. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied. Firstly the vibro-impact system in a form of moling device was modelled and analysed to understand how the progression rates can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces (no contact, contact with progression and contact without progression). In the second application frictional chatter occurring during metal cutting has been examined via numerical simulation method. The analysis has shown that the bifurcation analysis can be very useful to make an appropriate choice of the system parameters to avoid chatter. The last problem comes from rotordynamics, where nonlinear interaction between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation.Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM2006-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782006000400018Journal of the Brazilian Society of Mechanical Sciences and Engineering v.28 n.4 2006reponame:Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/S1678-58782006000400018info:eu-repo/semantics/openAccessWiercigroch,Marianeng2007-10-08T00:00:00Zoai:scielo:S1678-58782006000400018Revistahttps://www.scielo.br/j/jbsmse/https://old.scielo.br/oai/scielo-oai.php||abcm@abcm.org.br1806-36911678-5878opendoar:2007-10-08T00:00Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false
dc.title.none.fl_str_mv Applied nonlinear dynamics of non-smooth mechanical systems
title Applied nonlinear dynamics of non-smooth mechanical systems
spellingShingle Applied nonlinear dynamics of non-smooth mechanical systems
Wiercigroch,Marian
Nonlinear dynamics
non-smooth systems
mechanical vibrations
title_short Applied nonlinear dynamics of non-smooth mechanical systems
title_full Applied nonlinear dynamics of non-smooth mechanical systems
title_fullStr Applied nonlinear dynamics of non-smooth mechanical systems
title_full_unstemmed Applied nonlinear dynamics of non-smooth mechanical systems
title_sort Applied nonlinear dynamics of non-smooth mechanical systems
author Wiercigroch,Marian
author_facet Wiercigroch,Marian
author_role author
dc.contributor.author.fl_str_mv Wiercigroch,Marian
dc.subject.por.fl_str_mv Nonlinear dynamics
non-smooth systems
mechanical vibrations
topic Nonlinear dynamics
non-smooth systems
mechanical vibrations
description This paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspaceomega. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied. Firstly the vibro-impact system in a form of moling device was modelled and analysed to understand how the progression rates can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces (no contact, contact with progression and contact without progression). In the second application frictional chatter occurring during metal cutting has been examined via numerical simulation method. The analysis has shown that the bifurcation analysis can be very useful to make an appropriate choice of the system parameters to avoid chatter. The last problem comes from rotordynamics, where nonlinear interaction between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation.
publishDate 2006
dc.date.none.fl_str_mv 2006-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782006000400018
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dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1678-58782006000400018
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 Engenharia e Ciências Mecânicas - ABCM
publisher.none.fl_str_mv Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
dc.source.none.fl_str_mv Journal of the Brazilian Society of Mechanical Sciences and Engineering v.28 n.4 2006
reponame:Journal of the Brazilian Society of Mechanical Sciences and Engineering (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 Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)
collection Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)
repository.name.fl_str_mv Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)
repository.mail.fl_str_mv ||abcm@abcm.org.br
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