Nonlinear Dynamics

, Volume 92, Issue 3, pp 961–971 | Cite as

Assessment of the harmonic balance method on a self-oscillating one-degree-of-freedom system with regularized friction

  • Pierre Vigué
  • Christophe Vergez
  • Sami Karkar
  • Bruno Cochelin
Original Paper


Time-periodic solutions of dynamical systems can be looked for using a discretization method. This paper tests the harmonic balance method (HBM) on a one-degree-of-freedom system (mass, damper, spring, belt) with a regularized friction law. Its relative error is computed with respect to the number of discretization unknowns. Despite the widespread idea that frequency methods are hardly applicable to friction problems, the HBM compares well with a classical time-domain method for this nonlinear system. The main conclusion of this article is that the HBM, without any specific optimization, is well suited for regularized friction.


Nonlinear dynamics Harmonic balance method Orthogonal collocation method Periodic solutions Friction Numerical continuation 



This work has been carried out in the framework of the Labex MEC (ANR-10-LABX-0092). The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille University— A\(^*\)MIDEX, a French “Investissements d’Avenir” programme.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Pierre Vigué
    • 1
  • Christophe Vergez
    • 1
  • Sami Karkar
    • 2
  • Bruno Cochelin
    • 1
  1. 1.LMA, Centrale Marseille, CNRSAix Marseille UnivMarseilleFrance
  2. 2.Ecole Centrale de LyonEcully CedexFrance

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