Periodic solutions of a two-degree-of-freedom autonomous vibro-impact oscillator with sticking phases

Huong Le Thi 1, 2 Stéphane Junca 1, 2 Mathias Legrand 3
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : This contribution explores the free dynamics of a simple two-degree-of-freedom vibro-impact oscillator. One degree-of-freedom is limited by the presence of a rigid obstacle and periodic solutions involving one sticking phase per period (1-SPP) are targeted. A method to obtain such orbits is proposed: it provides conditions on the existence of 1-SPP as well as closed form solutions. It is shown that 1-SPP might not exist for a given combination of masses and stiffnesses. The set of 1-SPP is at most a countable set of isolated periodic orbits. The construction of 1-SPP requires numerical developments that are illustrated on a few relevant examples. Comparison with nonlinear modes of vibration involving one impact per period (1-IPP) is also considered. Interestingly, an equivalence between 1-SPP and a special set of isolated 1-IPP is established. It is also demonstrated that the prestressed system features sticking phases of infinite duration.

A few SPP orbits are animated below (click right -> view image for optimal quality).
  • Simplest SPP
  • SPP with distinct masses but same stiffnesses
  • SPP with same masses but distinct stiffnesses
  • SPP with initial "negative" gap: sticking phase of infinite duration
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Contributeur : Mathias Legrand <>
Soumis le : vendredi 19 janvier 2018 - 16:18:47
Dernière modification le : mardi 23 janvier 2018 - 19:07:11

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Huong Le Thi, Stéphane Junca, Mathias Legrand. Periodic solutions of a two-degree-of-freedom autonomous vibro-impact oscillator with sticking phases. Nonlinear Analysis: Hybrid Systems, Elsevier, 2018, 28, pp.54-74. 〈10.1016/j.nahs.2017.10.009〉. 〈hal-01305719v2〉

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