One-dimensional granular chains as transmitted force attenuators

We design a one-dimensional granular container in the form of a granular chain to reduce the force transmitted to a fixed barrier at its boundary. The granular chain considered is composed of ordered “heavy” and “light” beads (granules), and possesses strongly nonlinear acoustics due to Hertzian interactions, as well as zero tensile strength resulting in bead separations and subsequent collisions. We find the relationship between the transmitted force and the mass ratio of light beads to heavy beads and the relationship between the transmitted force and the number of beads in each subchain. We obtain an optimal design to minimize the transmitted force under the condition of a fixed total length of the chain. Computational predictions are validated by experiments, wherein we also estimate (i) the value of the damping between beads and (ii) the linear stiffness between the end bead and the barrier at the boundary of the granular chain. Transient, propagating localized oscillations are found in this system in both simulations and experiments, which result due to the strong nonlinearity of the granular chain. These results offer the possibility of systematically designing granular shock absorbers of enhanced performance compared to their linear counterparts.