Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems. (1st May 2017)

• Record Type: Journal Article
• Authors: Xie, L.; Baguet, S.; Prabel, B.; Dufour, R.
• Is Part Of: Mechanical systems and signal processing. Volume 88(2017)
• Page Start: 445
• Page End: 461
• Publication Date: 2017-05-01
• Subjects: Harmonic balance method -- Periodic solutions -- Quasiperiodic solutions -- Continuation -- Bifurcation tracking -- Limit point -- Neimark-Sacker bifurcation -- Floquet exponents -- Nonlinear energy sink -- Jeffcott rotor; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2016.09.037
• Languages: English
• ISSNs: 0888-3270

Abstract

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. Abstract : Highlights: A frequency domain method for bifurcation analysis of nonlinear dynamical systems is developed. The proposed method consists in directly tracking the bifurcation points when a system parameter is varied. The method is based on extended systems, Harmonic Balance Method and arc-length continuation. An original extended system for the detection and tracking of Neimark-Sacker (secondary Hopf) bifurcations is introduced. With only one computation a map showing the stability boundaries and changes of dynamical regime is obtained.