Nonlinear Hysteretic Torsional Waves.
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 to be 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 types 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.
LUNAM Universités, CNRS, Université du Maine, LAUM UMR-CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans, France.
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Cabaret
LUNAM Universités, CNRS, Université du Maine, LAUM UMR-CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans, France.
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Béquin
LUNAM Universités, CNRS, Université du Maine, LAUM UMR-CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans, France.
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Theocharis
Acoustics Department, Faculty of Physics, Moscow State University, 119991 Moscow, Russia.
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Andreev
LUNAM Universités, CNRS, Université du Maine, LAUM UMR-CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans, France.
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Gusev
LUNAM Universités, CNRS, Université du Maine, LAUM UMR-CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans, France.
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Tournat
D061725:Accelerometry / Q000379:methods; D060733:Electromagnetic Radiation; D059346:Magnets; D008962:Models, Theoretical; D017711:Nonlinear Dynamics