By using numerical simulation, the kinetic energy/temperature, the energy dissipation and the volume fraction in a 1D vertical vibrational bed are studied. Discrete element simulation shows that the granular bed moves up and down as an ensemble and the kinetic energy of the particles increases along the bed height when the bed bottom vibrates at a low-frequency and low-amplitude. For high-frequency vibrations, the particles in the bed move randomly and their kinetic energy decreases along the bed height. The energy dissipation and the volume fraction of the particles are also influenced by the vibrations frequency obviously, and they show different distributions at the high and low frequencies. In addition, we have compared the result of the discrete element simulation with that of the hydrodynamic simulation. When the bed bottom vibrates at high frequency, the two simulation methods can get the similar results. However, for the low-frequency and low-amplitude vibrations, the computed results are opposite to each other. Since the particles in the bed do not move and collide randomly, the application of the hydrodynamic simulation to the bed with low-frequency and low-amplitude vibrations should be investigated and discussed further.