SOME ENERGY CONSERVATIVE SCHEMES FOR VIBRO-IMPACTS OF A BEAM ON RIGID OBSTACLES

Cédric Pozzolini (1, 2) , Michel Salaün (3)

1 CNES - Centre National d'Études Spatiales [Toulouse]
2 INSA Lyon - Institut National des Sciences Appliquées de Lyon
3 ICA - Institut Clément Ader

Caused by the problem of unilateral contact during vibrations of satellite solar arrays, the aim of this paper is to better understand such a phenomenon. Therefore, it is studied here a simplified model composed by a beam moving between rigid obstacles. Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of non-penetration Signorini's conditions. For this, starting from the works of Dumont and Paoli, we adapt to our beam model the singular dynamic method introduced by Renard. A particular emphasis is given in the use of a restitution coefficient in the impact law. Finally, various numerical results are presented and energy conservation capabilities of the schemes are investigated.

Mots clés: Elastic beam; Finite element method; Variational inequalities; Unilateral constraints; Dynamics; Restitution coefficient

Domaines: Analyse numérique [math.NA]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Cédric Pozzolini, Michel Salaün. SOME ENERGY CONSERVATIVE SCHEMES FOR VIBRO-IMPACTS OF A BEAM ON RIGID OBSTACLES. ESAIM: Mathematical Modelling and Numerical Analysis, 2011, vol. 45, pp.1163-1192. ⟨10.1051/m2an/2011008⟩. ⟨hal-00618768⟩