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Bifurcation analysis of Nonlinear Normal Modes with the Harmonic Balance Method

Abstract : This work presents a frequency-domain method based on the Harmonic Balance Method (HBM) to perform bifurcation and stability analysis of Nonlinear Normal Modes (NNM). To do so, a frequency phase condition has been adapted from time domain in order to fix the non-uniqueness of the solution of the autonomous equation of motion. Then, a small damping coefficient has been introduced in the equation of motion to make invertible the matrices used during the pseudo-arc length continuation process. Finally, a shifted quadratic eigenvalue problem has been used to perform stability and bifurcation analysis. The resulting HBM-based algorithm permits the continuation of NNMs, the precise computation of bifurcation points as well as branch switching.
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Clément Grenat, Sébastien Baguet, Régis Dufour, Claude-Henri Lamarque. Bifurcation analysis of Nonlinear Normal Modes with the Harmonic Balance Method. ENOC 2017, 9th European Nonlinear Dynamics Conference, Jun 2017, Budapest, Hungary. ⟨hal-01667951⟩

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