An existence result for non-smooth vibro-impact problems

Laetitia Paoli (1)

1 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne

We are interested in mechanical systems with a finite number of degrees of freedom submitted to frictionless unilateral constraints. We consider the case of a convex, non-smooth set of admissible positions given by $K =\{q ∈\mathbb R^d ; \phi_\alpha(q)\geq 0, 1\leq \alpha\leq v \}$, $v\geq 1$, and we assume inelastic shocks at impacts. We propose a time-discretization of the measure differential inclusion which describes the dynamics and we prove the convergence of the approximate solutions to a limit motion which satisfies the constraints. Moreover, if the geometric properties ensuring continuity on data hold at the limit, we show that the transmission of velocities at impacts follows the inelastic shocks rule.

Mots clés: Vibro-impact; Non-smooth convex constraints; Measure differential inclusion; Inelastic shocks; Time-discretization scheme; Convergence; Existence

Domaines: Mathématiques [math]

Laetitia Paoli. An existence result for non-smooth vibro-impact problems. Journal of Differential Equations, 2005, 211 (2), pp.247-281. ⟨10.1016/j.jde.2004.11.008⟩. ⟨hal-01569156⟩