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Journal Articles Mechanical Systems and Signal Processing Year : 2017

Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems

Abstract

The aim of this paper is to provide an efficient frequency-domain method for bifurcation analysis of nonlinear dynamical systems. The proposed method consists in directly tracking the bifurcation points when a system parameter such as the excitation or nonlinearity level is varied. To this end, a so-called extended system comprising the equation of motion and an additional equation characterizing the bifurcation of interest is solved by means of the Harmonic Balance Method coupled with an arc-length continuation technique. In particular, an original extended system for the detection and tracking of Neimark-Sacker (secondary Hopf) bifurcations is introduced. By applying the methodology to a nonlinear energy sink and to a rotor-stator rubbing system, it is shown that the bifurcation tracking can be used to efficiently compute the boundaries of stability and/or dynamical regimes, i.e., safe operating zones.
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Dates and versions

hal-01402109 , version 1 (24-11-2016)

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Lihan Xie, Sébastien Baguet, Benoit Prabel, Régis Dufour. Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems. Mechanical Systems and Signal Processing, 2017, 88, pp.445-461. ⟨10.1016/j.ymssp.2016.09.037⟩. ⟨hal-01402109⟩
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