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.