Exciting and Harvesting Vibrational States in Harmonically Driven Granular Chains

TL;DR

This paper investigates how harmonic excitation can excite various vibrational states in granular chains, combining theory and experiments, and explores their potential for vibration energy harvesting.

Contribution

It demonstrates the excitation of multiple vibrational states in granular chains and validates the nonlinear Schrödinger equation's predictions, proposing applications in energy harvesting.

Findings

Multiple vibrational states can be excited in granular chains.

The nonlinear Schrödinger equation accurately predicts certain modes.

The electromechanical model matches experimental energy conversion results.

Abstract

This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multi-modal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the Nonlinear Schrodinger (NLS) equation predicts the corresponding modes fairly well. We propose that nonlinear multi-modal systems can be useful in vibration energy harvest- ing and discuss a prototypical framework for its realization. The electromechanical model we derive predicts accurately the conversion from mechanical to electrical energy observed in the experiments.