On the periodic motions of a one-degree-of-freedom oscillator

• Robert Kooij ^[1] ; André Zegeling ^[2]
  1. [1] Delft University of Technology

     Delft University of Technology

     Países Bajos

     
  2. [2] Guangxi Normal University

     Guangxi Normal University

     China

     
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. 3, 2024, págs. 479-494
• Idioma: inglés
• DOI: 10.1007/s40324-023-00335-3
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• Resumen

  • We present a mechanical model for an oscillator with one degree of freedom under the influence of a flowing medium. Under fairly general conditions we show that the ensuing differential equation has at most two limit cycles and we give examples where exactly two limit cycles will occur. The implications of this result are that it is possible for a system of this kind to exhibit galloping even when the so-called Den Hartog criterion of local instability is not satisfied.