Effects of uncertainties on pulse attenuation in dimer granular chains with and without pre-compression

In this work, the effects of inherent variability of the geometric properties of dimer granular chains on their capacity to passively attenuate propagating pulses are investigated. Numerical studies are performed for both the nominal model and the system with uncertainty. The deterministic system is governed by a single parameter (the ratio of the radii of “heavy” and “light” beads of the dimer) and is fully rescalable with energy. The effects of uncertainty, i.e., of the spatial variability of the radii of the light (odd) beads of the granular chain, on the transmitted force at its boundary are investigated. Reliability analysis through Monte Carlo simulations and sensitivity analysis of the dimer with uncertain properties are carried out, and a deeper insight for improved bead configurations is provided. It is shown that the optimal level of force attenuation achieved with a deterministically predicted optimal parameter can be further increased when certain spatial variations in the parameter, based on specific wave number content, are introduced.