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
Liste complète des métadonnées
Contributeur : Mathias Legrand <>
Soumis le : jeudi 21 avril 2016 - 17:08:09
Dernière modification le : mercredi 12 avril 2017 - 01:10:04
Document(s) archivé(s) le : mardi 15 novembre 2016 - 09:25:16


Distributed under a Creative Commons Paternité - Partage selon les Conditions Initiales 4.0 International License


  • HAL Id : hal-01305719, version 1



Huong Le Thi, Stéphane Junca, Mathias Legrand. Periodic solutions of a two-degree-of-freedom autonomous vibro-impact oscillator with sticking phases. 2016. <hal-01305719>



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