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Micro-slip as a loss of determinacy in dry-friction oscillators

Research output: Contribution to journalArticle

Original languageEnglish
Article number1930015
Number of pages21
JournalInternational Journal of Bifurcation and Chaos
Volume29
Issue number6
DOIs
DateAccepted/In press - 23 Nov 2018
DatePublished (current) - 15 Jun 2019

Abstract

Dry-friction contacts in mechanical oscillators can be modeled using nonsmooth differential equations, and recent advances in dynamical theory are providing new insights into the stability and uniqueness of such oscillators. A classic model is that of spring-coupled masses undergoing stick-slip motion on a rough surface. Here, we present a phenomenon in which multiple masses transition from stick to slip almost simultaneously, but suffer a brief loss of determinacy in the process. The system evolution becomes many-valued, but quickly collapses back down to an infinitesimal set of outcomes, a sort of "micro-indeterminacy". Though fleeting, the loss of determinacy means masses may each undergo different microscopic sequences of slipping events, before all masses ultimately slip. The microscopic loss of determinacy is visible in local changes in friction forces, and in creating a bistability of global stick-slip oscillations. If friction forces are coupled between the oscillators then the effect is more severe, as solutions are compressed instead onto two (or more) macroscopically different outcomes.

    Research areas

  • bifurcation, chaos, Discontinuity, friction, oscillators, sliding, slip, sticking, switching

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via World Scientific at https://doi.org/10.1142/S0218127419300155 . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 1 MB, PDF document

    Embargo ends: 15/06/20

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    Licence: Other

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