  We consider the penetration dynamics of a vertical cylinder into a dry
granular medium subjected to successive impacts. The depth of the impactor
below the free surface $z_N$ first evolves linearly with the impact number $N$
and then follows a power-law evolution $z_N \propto N^{1/3}$. The depth reached
by the cylinder after a given number of impacts is observed to increase with
the impact energy but to decrease with its diameter and the density of the
granular medium. We develop a model that accounts for the quasi-static and
inertial granular forces applying on the cylinder to rationalize our
observations. This approach reveals the existence of two intrusion regimes for
large and small impact numbers, allowing all data to be rescaled on a master
curve. Then, we extend the study to the effect of sidewalls on the dynamics of
the impactor. We show that lateral confinement changes the dependence of the
impactor depth on the impact number $z_N (N)$. This effect is accounted for by
considering the increase of the granular drag with the lateral confinement.
