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

By T. Detroux, Ludovic Renson, Luc Masset, Gaetan Kerschen. 2015

282 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering, Civil and Structural Engineering

View Paper: https://www.semanticscholar.org/paper/f8823b05b2507be88a8b00f58256f4b8d9a93015

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Citations in the corpus

• Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems (2017, background): “The second approach relies on bordering techniques and minimally extended systems in which only one scalar function is added [32, 40, 47].”