Graphene is a two-dimensional (2D) hexagonal array of carbon atoms in sp2-hybridized states. Graphene presents unique and exceptional electronic, thermal and mechanical properties. However, in its pristine state graphene is a gapless semiconductor, which poses some limitations to its use in some transistor electronics. Because of this there is a renewed interest in other possible two-dimensional carbon-based structures similar to graphene. Examples of this are graphynes and graphdiynes, which are two-dimensional structures, composed of carbon atoms in sp2 and sp-hybridized states. Graphdiynes (benzenoid rings connecting two acetylenic groups) were recently synthesized and they can be intrinsically nonzero gap systems. These systems can be easily hydrogenated and the amount of hydrogenation can be used to tune the band gap value. In this work we have investigated, through fully atomistic molecular dynamics simulations with reactive force field (ReaxFF), the structural and dynamics aspects of the hydrogenation mechanisms of graphdiyne membranes. Our results showed that depending on whether the atoms are in the benzenoid rings or as part of the acetylenic groups, the rates of hydrogenation are quite distinct and change in time in a very complex pattern. Initially, the most probable sites to be hydrogenated are the carbon atoms forming the triple bonds, as expected. But as the amount of hydrogenation increases in time this changes and then the carbon atoms forming single bonds become the preferential sites. The formation of correlated domains observed in hydrogenated graphene is no longer observed in the case of graphdiynes. We have also carried out ab initio DFT calculations for model structures in order to test the reliability of ReaxFF calculations.