Complex nonlinear response of a piecewise linear oscillator: Experiment and simulation

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this work an experimental piecewise linear oscillator is presented. This consists of a linear mass-spring-damper undergoing intermittent contact with a slender beam, which can be modelled as providing stiffness support only. Experimental bifurcation diagrams are presented in which a complex response is observed. Smooth bifurcations are recorded, but more typically rapid transitions between at-tractors were observed. All of the following are shown to occur: coexisting attrac-tors, basin erosion associated with grazing trajectories, pairs of unstable periodic orbits, chaotic response, loss of stability through grazing and saddle node bifurcations. All of these come into play to generate the observed experimental bifurcation scenarios. It is shown that a global analysis is important in understanding the system response, especially close to grazing conditions. Although grazing is known to cause a local change in stability, it was found that more often grazing of one orbit would cause a change in the other orbits which resulted in boundary crisis and annihilation of the attractor.
Original languageEnglish
Title of host publicationIUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments
Subtitle of host publicationProceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, Held in Budapest, Hungary, June 7–11, 2010
EditorsGabor Stepan, Laszlo L. Kovacs, Andras Toth
PublisherSpringer Netherlands
Pages135-143
Number of pages9
Volume30
ISBN (Electronic)978-94-007-1643-8
ISBN (Print)9789400716421
DOIs
Publication statusPublished - 2011
EventIUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, 2010 - Budapest, Hungary
Duration: 7 Jun 201011 Jun 2010

Publication series

NameIUTAM Bookseries
PublisherSpringer Netherlands
ISSN (Print)1875-3507

Conference

ConferenceIUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, 2010
CountryHungary
CityBudapest
Period7/06/1011/06/10

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    Ing, J., Pavlovskaia, E., & Wiercigroch, M. (2011). Complex nonlinear response of a piecewise linear oscillator: Experiment and simulation. In G. Stepan, L. L. Kovacs, & A. Toth (Eds.), IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments: Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, Held in Budapest, Hungary, June 7–11, 2010 (Vol. 30, pp. 135-143). (IUTAM Bookseries). Springer Netherlands. https://doi.org/10.1007/978-94-007-1643-8_16