Tunable vibrational band gaps in one-dimensional diatomic granular crystals with three-particle unit cells

We investigate the tunable vibration filtering properties of statically compressed one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (sphere-cylinder-sphere) in which the length of the cylinder is varied systematically. We investigate the response of these granular crystals, given small amplitude dynamic displacements relative to those due to the static compression, and characterize their linear frequency spectrum. We find good agreement between theoretical dispersion relation analysis (for infinite systems), state-space analysis (for finite systems), and experiments. We report the observation of three distinct pass bands separated by two finite band gaps, and show their tunability for variations in cylinder length and static compression. (C) 2011 American Institute of Physics. [doi:10.1063/1.3556455]