The physisorption of atomic hydrogen on graphene is investigated quantum mechanically using a semiempirical model for the lattice dynamics. A thermally averaged wave packet propagation describes the motion of the H atoms with respect to the membrane. Two graphene configurations, either supported on a silicone oxide substrate or suspended over a hole in the substrate, are considered. In both cases, the phonon spectrum is modified in such a way that graphene is stabilized with respect to thermal fluctuations. The sticking probabilities of hydrogen on these stabilized membranes at 10 K are high at low collision energies, and larger than on graphite.