Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles.

*(English)*Zbl 1451.74209Summary: 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.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |

74H45 | Vibrations in dynamical problems in solid mechanics |

35L85 | Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |