Experimental bifurcation analysis of an impact oscillator – Determining stability

Publication: Research - peer-reviewJournal article – Annual report year: 2014

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We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior. As a proof of concept the three methods are successfully implemented and tested for a harmonically forced impact oscillator with a hardening spring nonlinearity, and controlled by electromagnetic actuators. We show that under certain conditions it is possible to quantify the instability in terms of finite-time Lyapunov exponents. As a special case we study an isolated branch in the bifurcation diagram brought into existence by a 1:3 subharmonic resonance. On this isola it is only possible to determine stability using one of the three methods, which is due to the fact that only this method guarantees that the equilibrium state can be restored after measuring stability.
Original languageEnglish
JournalJournal of Sound and Vibration
Volume333
Issue number21
Pages (from-to)5464–5474
ISSN0022-460X
DOIs
StatePublished - 2014
CitationsWeb of Science® Times Cited: 11
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