Experimental tracking of limit-point bifurcations and backbone curves using control-based continuation

Ludovic Renson, David Barton, Simon Neild

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)
283 Downloads (Pure)

Abstract

Control-based continuation (CBC) is a means of applying numerical continuation directly to a physical experiment for bifurcation analysis without the use of a mathematical model. CBC enables the detection and tracking of bifurcations directly, without the need for a post-processing stage as is often the case for more traditional experimental approaches. In this paper, we use CBC to directly locate limit-point bifurcations of a periodically forced oscillator and track them as forcing parameters are varied. Backbone curves, which capture the overall frequency-amplitude dependence of the system’s forced response, are also traced out directly. The proposed method is demonstrated on a single-degree-of-freedom mechanical system with a nonlinear stiffness characteristic. Results are presented for two configurations of the nonlinearity — one where it exhibits a hardening stiffness characteristic and one where it exhibits softening-hardening.
Original languageEnglish
Article number1730002
Number of pages19
JournalInternational Journal of Bifurcation and Chaos
Volume27
Issue number1
Early online date1 Nov 2016
DOIs
Publication statusPublished - Jan 2017

Keywords

  • control-based continuation
  • experimental bifurcation analysis
  • bifurcation tracking
  • backbone curves
  • softening-hardening nonlinearity

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