Resonance effects on the dynamics of dense granular beds: Achieving optimal energy transfer in vibrated granular systems

Using a combination of experimental techniques and discrete particle method simulations, we investigate the resonant behaviour of a dense, vibrated granular system. We demonstrate that a bed of particles driven by a vibrating plate may exhibit marked differences in its internal energy dependent on the specific frequency at which it is driven, even if the energy corresponding to the oscillations driving the system is held constant and the acceleration provided by the base remains consistently significantly higher than the gravitational acceleration, g. We show that these differences in the efficiency of energy transfer to the granular system can be explained by the existence of resonances between the bed's bulk motion and that of the oscillating plate driving the system. We systematically study the dependency of the observed resonant behaviour on the system's main, controllable parameters and, based on the results obtained, propose a simple empirical model capable of determining, for a given system, the points in parameter space for which optimal energy transfer may be achieved.