Particle dynamics modeling is done to study the behavior of granular beds subjected to vibrations imposed by a plane boundary which oscillates sinusoidally about a zero mean speed. Significant differences between the lower and higher shaking acceleration regions are found for the granular temperature and solids fraction depth profiles, which characterize the effectiveness of the boundary in fluidizing the beds. When higher accelerations are applied, the temperature is maximum at the vibrating floor and attenuates through the depth, while the solids fraction profiles exhibit a maximum at some intermediate depth. At lower acceleration values, most of the mass is located near the bottom, and fluidization occurs on the top, where a high temperature and low solids fraction is found, Simulation results are in good agreement with the kinetic theory predictions of Richman et al. in the higher acceleration regions and quantitatively consistent with the experimental data of Hunt et al. in the lower accelerations. Diffusion coefficients, computed using both the velocity autocorrelation function and the Einstein relation, are in agreement with each other and with the theoretical predictions of Savage. Critical conditions to produce a convective flow and associated segregation phenomena in a frictional bed are carefully investigated. The cell size, friction coefficient, agitation amplitude and acceleration are found to be the crucial factors. The first observation in simulation of an arching movement near the bottom of a large cell is also reported.