  We study the existence of periodic solutions in a class of planar Filippov
systems obtained from non-autonomous periodic perturbations of reversible
piecewise smooth differential systems. It is assumed that the unperturbed
system presents a simple two-fold cycle, which is characterized by a closed
trajectory connecting a visible two-fold singularity to itself. It is shown
that under certain generic conditions the perturbed system has sliding and
crossing periodic solutions. In order to get our results, Melnikov's ideas were
applied together with tools from the geometric singular perturbation theory.
Finally, a study of a perturbed piecewise Hamiltonian model is performed.
