  Molecular dynamical (MD) simulations are performed to simulate two
dimensional vibrofluidized granular materials in this work. Statistics on
simulation results indicate that there exist shocks propagating upward in each
vibrating cycle. Under certain driving parameters surface waves similar to
Faraday instability in normal fluid coexist with internal waves. Relationship
between the two kinds of waves is explored. Moreover simulation results
indicate that periodically structured bottom can change the dispersion
relationship and amplitude of surface waves.
