Sub-harmonic resonant solutions of a harmonically excited dry friction oscillator

G. Csernák, G. Stépán, S. W. Shaw

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20 Citations (Scopus)


Special sub-harmonic solutions of a harmonically forced dry-friction oscillator are analysed. Although the typical non-sticking solutions are stable and symmetric, a continuum of possible asymmetric, marginally stable solutions exist at excitation frequencies Ω = 1/2n. We determine the explicit form of the one-parameter family of these solutions, and give the conditions under which our formulae are valid. The stability of the solutions is examined in the third-order approximation. Finally, our analytical results are checked by numerical simulations.

Original languageEnglish
Pages (from-to)93-109
Number of pages17
JournalNonlinear Dynamics
Issue number1-2
Publication statusPublished - Oct 1 2007



  • Asymmetric solutions
  • Coexisting solutions
  • Coulomb friction
  • Marginal stability
  • Normal form transformation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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