Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals with Three-Particle Unit Cells

TL;DR

This study explores how one-dimensional diatomic granular crystals with three-particle unit cells can have their vibrational band gaps tuned through structural and static compression adjustments, combining theoretical, numerical, and experimental methods.

Contribution

It introduces a systematic approach to tuning vibrational band gaps in granular crystals with three-particle units, validated by theory, simulations, and experiments.

Findings

Up to three pass bands identified.

Two finite band gaps observed.

Band gaps tunable via cylinder length and static compression.

Abstract

We investigate the tunable vibration filtering properties of 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 (steel-cylinder-sphere) in which the length of the cylinder is varied systematically. We apply static compression to linearize the dynamic response of the crystals 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 up to three distinct pass bands and two finite band gaps and show their tunability for variations in cylinder length and static compression.