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On some periodic solutions of discrete vibro-impact systems with a unilateral contact condition

Abstract : The mechanical motivation is presented for a PDE with a constraint. The purpose of this thesis is to study N degree-of-freedom vibro-impact systems with an unilateral contact. The resulting system is linear in the absence of contact; it is governed by an impact law otherwise. The author identifies some nonlinear modes that display a sticking phase. The First Return Map is a fundamental tool to explore periodic solutions. Since the Poincaré section is a subset of the contact interface in the phase-space, it can be tangent to orbits which yields the well-known square-root singularity. This singularity is here revisited in a rigorous mathematical framework. Moreover, the study of this singularity implies a more important singularity: the discontinuity of the first return time. Finally, the square-root dynamics near the linear grazing modes which may lead to the instability of these linear grazing modes is studied.
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Huong Le Thi. On some periodic solutions of discrete vibro-impact systems with a unilateral contact condition. General Mathematics [math.GM]. Université Côte d'Azur, 2017. English. ⟨NNT : 2017AZUR4033⟩. ⟨tel-01665818⟩

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