Nonlinear Pulse Equi-partition in Weakly Coupled Ordered Granular Chains with no Pre-Compression

Abstract: We report on the strongly nonlinear dynamics of an array of weakly coupled, non-compressed, parallel granular chains subject to a local initial impulse. The motion of the granules in each chain is constrained to be in one direction which coincides with the orientation of the chain. We show that in spite of the fact that the applied impulse is applied to a one of the granular chains, the resulting pulse that initially propagating only in the excited chain gets gradually equi-partitioned between its neighboring chains, and eventually in all chains of the array. In particular, the initially strongly localized state of energy distribution evolves towards a final stationary state of formation of identical solitary waves that propagate in each one of the chains. These solitary waves are synchronized and have identical speeds. We show that the phenomenon of primary pulse equi-partition between the weakly coupled granular chains can be fully reproduced in coupled binary models which constitute a significantly simpler model that captures the main qualitative features of the dynamics of the granular array. The results reported herein are of major practical significance, since it indicates that the weakly coupled array of granular chains is a medium in which an initially localized excitation gets gradually defocused, resulting in drastic reduction of propagating pulses as they are equi-partitioned among all chains.