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Suppression of limit cycle oscillations in the van der Pol oscillator by means of passive non-linear energy sinks

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dc.contributor.author Lee, YS en
dc.contributor.author Vakakis, AF en
dc.contributor.author Bergman, LA en
dc.contributor.author McFarland, DM en
dc.date.accessioned 2014-03-01T01:25:14Z
dc.date.available 2014-03-01T01:25:14Z
dc.date.issued 2006 en
dc.identifier.issn 1545-2255 en
dc.identifier.uri http://hdl.handle.net/123456789/17604
dc.subject LCO suppression en
dc.subject Limit cycle oscillation (LCO) en
dc.subject Non-linear energy sink (NES) en
dc.subject Numerical continuation en
dc.subject Resonance capture en
dc.subject Van der Pol oscillator en
dc.subject.classification Construction & Building Technology en
dc.subject.classification Engineering, Civil en
dc.subject.classification Instruments & Instrumentation en
dc.subject.other Bifurcation (mathematics) en
dc.subject.other Computational methods en
dc.subject.other Degrees of freedom (mechanics) en
dc.subject.other Energy transfer en
dc.subject.other Oscillators (mechanical) en
dc.subject.other Parameter estimation en
dc.subject.other Robustness (control systems) en
dc.subject.other LCO suppression en
dc.subject.other Limit cycle oscillation (LCO) en
dc.subject.other Non-linear energy sink (NES) en
dc.subject.other Numerical continuation en
dc.subject.other Resonance capture en
dc.subject.other Van der Pol oscillator en
dc.subject.other Oscillations en
dc.title Suppression of limit cycle oscillations in the van der Pol oscillator by means of passive non-linear energy sinks en
heal.type journalArticle en
heal.identifier.primary 10.1002/stc.143 en
heal.identifier.secondary http://dx.doi.org/10.1002/stc.143 en
heal.language English en
heal.publicationDate 2006 en
heal.abstract We study suppression of the limit cycle oscillations (LCOs) of a van der Pol (VDP) oscillator, utilizing two configurations of non-linear energy sink (NES)-grounded and ungrounded. Through computational parameter studies we verify LCO elimination for certain ranges of NES parameters. Then, we establish the slow-flow equations to perform numerical and analytical studies of the transient and steady-state dynamics of the configuration studied. The transient dynamics turns out to involve resonance captures, through which irreversible, passive energy transfer (called non-linear energy pumping) is achieved frorn the VDP oscillator to the NES. We also perform computational bifurcation analysis by means of numerical continuation to gain some understanding of the dynamics of generation and elimination of non-linear energy pumping. The steady-state dynamics shows that the system may possess either subcritical or supercritical LCOs, leading to different degrees of robustness of suppression. The results reported in this work support the applicability of the NES concept to suppression of instabilities in self-excited systems. Copyright (c) 2005 John Wiley & Sons, Ltd. en
heal.publisher JOHN WILEY & SONS LTD en
heal.journalName Structural Control and Health Monitoring en
dc.identifier.doi 10.1002/stc.143 en
dc.identifier.isi ISI:000235587600005 en
dc.identifier.volume 13 en
dc.identifier.issue 1 en
dc.identifier.spage 41 en
dc.identifier.epage 75 en


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