Impulse Absorption by Tapered Alignments of Elastic Spheres

A numerical parametric study of 1D granular systems with Hertzian spheres is investigated. The relevant and always-repulsive interaction potential is nonlinearly dependent upon the overlap of adjacent grains. Specifically, we report our extensive investigation of two distinct systems and provide hard- sphere approximations as well as results from the numerical solution to the equations of motion. Chains can be characterized by the number of grains, $N$, the successive decrease in particle size or tapering, $q$, and restitutive losses, $\omega$. By increasing the tapering, these chains act as shock absorbers by converting well-defined pulses into noise and spreading the energy among all members in the chain.