Numerical simulation of a model of vibrations with joint clearance

Yves Dumont (1) , Laetitia Paoli (2)

1 LIM - Laboratoire d'Informatique et de Mathématiques
2 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne

Motivated by the problem of vibrations due to joint clearance between components in complex mechanical systems, we study in this paper the motion of a beam between rigid obstacles. We assume that the material is elastic and the motion is planar. The contact is described with a non-penetration condition, which leads to a model of dynamics with unilateral constraints. We propose a family of fully discretised approximations and their convergence is established. Moreover we present some examples of implementation using either finite element or spline space discretisation.

Mots clés: convergence; elastic beam; Signorini's conditions; time and space discretisations; vibrations with unilateral constraints

Domaines: Sciences de l'ingénieur [physics]; Mathématiques [math]; Vibrations [physics.class-ph]

Yves Dumont, Laetitia Paoli. Numerical simulation of a model of vibrations with joint clearance. International Journal of Computer Applications in Technology, 2008, 33 (1), pp.41-53. ⟨10.1504/IJCAT.2008.021884⟩. ⟨hal-01569160⟩