Elastic Wannier-Stark Ladders and Bloch Oscillations in 1D Granular Crystals

TL;DR

This study explores tunable elastic Wannier-Stark Ladders and Bloch Oscillations in a 1D granular chain, demonstrating experimental and numerical control over localized elastic energy modes with potential applications.

Contribution

It introduces a method to tune contact stiffness gradients in granular chains to realize and control elastic Wannier-Stark Ladders and Bloch Oscillations.

Findings

Resonant modes localized in space observed

Time-resolved Bloch Oscillations demonstrated

Tuning contact angles controls oscillation behavior

Abstract

We report the numerical and experimental study of elastic Wannier-Stark Ladders and Bloch Oscillations in a tunable one-dimensional granular chain consisting of cylindrical particles. The Wannier-Stark Ladders are obtained by tuning the contact angles to introduce a gradient in the contact stiffness along the granular chain. These ladders manifest as resonant modes localized in the space. When excited at the corresponding resonant frequencies, we demonstrate the existence of time-resolved Bloch Oscillations. The direct velocity measurements using Laser Doppler Vibrometry agree well with the numerical simulation results. We also show the possibility of further tailoring these Bloch Oscillations by numerical simulations. Such tunable systems could be useful for applications involving the spatial localization of elastic energy.