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Control-based continuation for investigating nonlinear experiments

Research output: Working paperWorking paper and Preprints

Original languageEnglish
Publication date2010
StatePublished

Abstract

This paper presents a systematic experimental study of two one-degree-of-freedom nonlinear devices using the newly introduced control-based continuation method by Sieber and Krauskopf [Nonlinear Dynamics 2008]. By considering hardening, softening and bistable spring characteristics we demonstrate the versitility and power of the control-based continuation method for investigating nonlinear experiments. We show that, using this method, it is possible to track the stable orbits of the devices through a saddle-node bifurcation (fold) where they lose stability and continue them up to the resonance peak where they undergo a second saddle-node bifurcation. For the bistable case, a bifurcation diagram is produced that is strongly reminiscent of the bifurcation diagram produced using the classical harmonic balance solution. A detailed introduction to general continuation methods is included to enable implementation by other experimentalists.

Additional information

Sponsorship: D.A.W. Barton gratefully acknowledges the support of Great Western Research in the provision of a research fellowship. B.P. Mann would like to acknowledge financial support from Dr. Ronald Joslin through an ONR Young Investigator Award. S.G. Burrows is supported by EPSRC grant EP/E044220/1.

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    Preprint (usually an early version) , 1013 KB, PDF-document

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