In this paper, the densification process experienced by a bed of frictional, inelastic spheres of diameter d in a rectangular vessel whose floor is subjected to high frequency (omega) and low amplitude (a/d not equal 0.1) sinusoidal oscillations is modeled using discrete element simulations. Our recent experimental observations as well as those in the literature motivate this investigation. Beginning with an initial random assembly resulting from gravity deposition, the floor motion activates the system so as to induce the formation of a distinct microstructure in the absence of a mean flow field. This is accompanied by an increase in coordination number and bulk solids fraction whose evolution is strongly dependent on the magnitude of the acceleration amplitude Gamma = a omega(2)/g.