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

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

Vibro-impact of a plate on rigid obstacles: existence theorem, convergence of a scheme and numerical simulations

The purpose of this paper is to describe a fully discrete approximation and its convergence to the continuum dynamical impact problem for the fourth-order Kirchhoff–Love plate model with nonpenetration Signorini contact condition. We extend to the case of plates the theoretical results of weak convergence due to Y. Dumont and L. Paoli, which was stated for Euler–Bernouilli beams. In particular, this provides an existence result for the solution of this problem. Finally, we discuss the numerical results we obtain

Energy conservative finite element semi-discretization for vibro-impacts of plates on rigid obstacles

Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of vibro-impact of plates between rigid obstacles with non-penetration Signorini’s conditions. To this aim, the dynamical Kirchhoff–Love plate model is considered and an extension to plates of the singular dynamic method, introduced by Renard and previously adapted to beams by Pozzolini and Salaün, is described. A particular emphasis is given in the use of an adapted Newmark scheme in which intervene a discrete restitution coefficient. Finally, various numerical results are presented and energy conservation capabilities of several numerical schemes are investigated and discussed

Numerical simulation of a model of vibrations with joint clearance

International audienceMotivated 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