Periodic solutions of a two-degree-of-freedom autonomous vibro-impact oscillator with sticking phases
Résumé
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
Fichier principal
1spphal.pdf (662.45 Ko)
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anim1.gif (460.28 Ko)
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anim2.gif (1.1 Mo)
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anim3.gif (586.01 Ko)
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anim4.gif (146.08 Ko)
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anim5.gif (171.89 Ko)
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hal-01305719.zip (4.31 Mo)
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