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Periodic self-modulation of an electrodynamically driven heated wire near resonance

Abstract : A thin nichrome wire driven near resonance by the Lorentz force and heated by an alternating electrical current is a popular lecture demonstration. Due to the convective cooling of the portions of the wire moving with the greatest amplitude, only glowing regions near a velocity node will be visible in a darkened room. Nonlinear effects and the thermal expansion coefficient of the wire displace the wire's tensioning mass. By adiabatic invariance, the work done on or by the vibrating wire, due to the changes in the mass's elevation, causes the natural frequency of the standing wave resonance to be shifted. Competition between the thermal inertia of the wire and the convective heat transfer coefficient introduces an exponential thermal relaxation time so that the amplitude of vibration is dependent on the ratio of the drive frequency to the changing resonance frequency at an earlier (retarded) time. These thermal and kinetic effects are incorporated into three coupled nonlinear ordinary differential equations that are separated by the method of multiple time scales and are solved numerically, reproducing both the spontaneous appearance of stable periodic amplitude modulation and the hysteretic behavior observed with increasing or decreasing of the drive frequency .
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https://hal-univ-lemans.archives-ouvertes.fr/hal-02057089
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Soumis le : mardi 5 mars 2019 - 09:57:10
Dernière modification le : jeudi 14 mars 2019 - 01:23:55
Archivage à long terme le : : jeudi 6 juin 2019 - 15:00:09

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Guillaume Penelet, Steven Garrett. Periodic self-modulation of an electrodynamically driven heated wire near resonance. Journal of the Acoustical Society of America, Acoustical Society of America, 2019, 145 (2), pp.998-1017. ⟨10.1121/1.5091094⟩. ⟨hal-02057089⟩

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