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Nonlinear Hysteretic Torsional Waves
J Cabaret1, P Béquin1, G Theocharis1
1LUNAM Universités, CNRS, Université du Maine, LAUM UMR-CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans, France.
Physical Review Letters
|August 15, 2015
Summary
We studied nonlinear hysteretic torsional pulses in magnetic beads. This research reveals unique pulse distortion and complex dynamics, offering insights into nonlinear wave control.
Area of Science:
- Physics
- Nonlinear Dynamics
- Materials Science
Background:
- Granular chains exhibit complex wave propagation phenomena.
- Nonlinear hysteretic behavior in contacts is crucial for understanding energy dissipation and wave distortion.
- Previous models often simplify or ignore hysteretic effects in granular systems.
Purpose of the Study:
- To theoretically and experimentally investigate nonlinear hysteretic torsional pulse propagation in a vertical granular chain.
- To characterize the unique pulse distortion and dynamic responses arising from hysteretic nonlinearity.
- To explore potential applications in nonlinear wave control devices.
Main Methods:
- Theoretical modeling of nonlinear hysteretic torsional coupling between beads.
- Experimental setup using a vertical chain of self-hanged magnetic beads.
- Analysis of pulse propagation, distortion, and dynamic responses using contact mechanics and hysteresis models (e.g., Preisach-Mayergoyz).
Main Results:
- Confirmed nonlinear hysteretic torsional coupling between magnetic beads.
- Observed unique nonlinear pulse distortion distinct from classical nonlinearities.
- Demonstrated complex dynamic responses dependent on wave history, consistent with hysteretic elasticity.
- Identified phenomena such as giant amplitude-dependent attenuation, short-term memory, and dispersive properties.
Conclusions:
- The magnetic bead granular chain provides a platform for studying nonlinear dynamic hysteresis without other material nonlinearities.
- The observed phenomena suggest potential applications in advanced nonlinear wave control devices, such as amplitude-dependent filters.
- This work advances the understanding of wave propagation in nonlinear and hysteretic systems.
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