Nonlinear Hysteretic Torsional Waves

TL;DR

This paper investigates the propagation of nonlinear hysteretic torsional pulses in a magnetic bead chain, revealing complex wave behaviors and potential applications in nonlinear wave control devices.

Contribution

It provides the first experimental and theoretical analysis of hysteretic nonlinear torsional wave propagation in granular chains, highlighting unique distortion and memory effects.

Findings

Nonlinear hysteretic torsional pulses exhibit complex distortion.

Wave response depends on the wave history, showing hysteresis.

Potential for amplitude-dependent wave filtering.

Abstract

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities, and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other type of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short term memory as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.