The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

T. Detroux*, Ludovic Renson, L. Masset, Gaetan Kerschen

*Corresponding author for this work

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

102 Citations (Scopus)
314 Downloads (Pure)

Abstract

The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection and tracking of bifurcations of nonlinear systems. To this end, an algorithm that combines the computation of the Floquet exponents with bordering techniques is developed. A new procedure for the tracking of Neimark-Sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed. The HB method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device.
Original languageEnglish
Pages (from-to)18-38
Number of pages21
JournalComputer Methods in Applied Mechanics and Engineering
Volume296
Early online date23 Jul 2015
DOIs
Publication statusPublished - 1 Nov 2015

Keywords

  • Bifurcation detection and tracking
  • Continuation of periodic solutions
  • Detached resonance curves
  • Floquet exponents
  • Harmonic balance
  • Quasiperiodic oscillations

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