Jumping Platonic Solids on a Vibrating Plate

The mechanical excitation of solid bodies by a vibrating plate is not only an interesting fundamental problem, but also has relevance in many mechanical systems, for example, in the preparation of granular gases in microgravity. Herein, the energy input by an oscillating plate is numerically investigated as a function of the excitation parameters for selected Platonic solids and their behavior compared to that of a jumping sphere. The most important additional features, not relevant for spheres, are the excitation of body rotations and a permanent energy exchange between the rotational and translational degrees of freedom during the collisions with the plate. The distribution of kinetic energies is analyzed by a numerical simulation of the dynamics, using structures which emulate the mechanical behavior of regular polyhedra. The mechanical excitation of macroscopic bodies by a vibrating ground plate is not only at the basis of numerous industrial applications, but it also has substantial academic interest, for instance in the fluidization of granular matter or the study of granular gases. While spherical bodies are considered in many studies in the past, the present paper examines Platonic solids in simulations and experiments. The coupling of rotational and translational degrees of freedom change the jump characteristics substantially.image