A convergence result for a vibro-impact problem with a general inertia operator

Raoul Dzonou (1) , Manuel Monteiro Marques (2) , Laetitia Paoli (1)

1 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne
2 ULISBOA - Universidade de Lisboa = University of Lisbon

We consider a mechanical system with a finite number of degrees of freedom and non-trivial inertia matrix, submitted to a single perfect unilateral constraint. We assume that the local impact law consists in the transmission of the tangential component of the velocity and the reflexion of the normal component which is multiplied by the restitution coefficient $e ∈ [0, 1]$. Then, starting from the measure-differential formulation of the problem given by J.J. Moreau, we propose a velocity-based time-stepping method, reminiscent of the catching-up algorithm for sweeping processes and we prove that the numerical solutions converge to a solution of the problem.

Mots clés: Vibro-impact dynamics; Measure differential inclusion; Sweeping process; Restitution coefficient

Domaines: Mathématiques [math]

Raoul Dzonou, Manuel Monteiro Marques, Laetitia Paoli. A convergence result for a vibro-impact problem with a general inertia operator. Nonlinear Dynamics, 2009, 2, pp.355-384. ⟨10.1007/s11071-009-9484-1⟩. ⟨hal-01552482⟩