Energy decay in a tapped granular column: Can a one-dimensional toy model provide insight into fully three-dimensional systems?

The decay of energy within particulate media subjected to an impulse is an issue of significant scientific interest, but also one with numerous important practical applications. In this paper, we study the dynamics of a granular system exposed to energetic impulses in the form of discrete taps from a solid surface. By considering a one-dimensional toy system, we develop a simple theory, which successfully describes the energy decay within the system following exposure to an impulse. We then extend this theory so as to make it applicable also to more realistic, three-dimensional granular systems, assessing the validity of the model through direct comparison with discrete particle method simulations. The theoretical form presented possesses several notable consequences; in particular, it is demonstrated that for suitably large systems, effects due to the bounding walls may be entirely neglected. We also establish the existence of a threshold system size above which a granular bed may be considered fully three dimensional.