A phenomenological model for predicting the effect of damping on wave turbulence spectra in vibrating plates

Thomas Humbert; C Josserand; Cyril Touzé; Olivier Cadot

A phenomenological model for predicting the effect of damping on wave turbulence spectra in vibrating plates

Thomas Humbert ^{1, 2, 3, *} C Josserand ² Cyril Touzé ^{1, 4} Olivier Cadot ^{1, 4}

* Corresponding author

1 UME - Unité de Mécanique

2 DALEMBERT - Institut Jean Le Rond d'Alembert

3 SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes

SPEC - UMR3680 - Service de physique de l'état condensé, IRAMIS - Institut Rayonnement Matière de Saclay

4 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles

Abstract : Thin plates vibrating at large amplitudes may exhibit a strongly nonlinear regime that has to be studied within the framework of wave turbulence. Experimental studies have revealed the importance of the damping on the spectra of wave turbulence , which precludes for a direct comparison with the theoretical results, that assumes a Hamiltonian dynamics. A phenomenological model is here introduced so as to predict the effect of the damping on the turbulence spectra. Self-similar solutions are found and the cutoff frequency is expressed as function of the damping rate and the injected power.

Keywords : wave turbulence thin plates vibrations phenomenological modal

Document type :

Conference papers

Domain :

Nonlinear Sciences [physics] / Chaotic Dynamics [nlin.CD]

Physics [physics] / Mechanics [physics] / Vibrations [physics.class-ph]

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A phenomenological model for predicting the effect of damping on wave turbulence spectra in vibrating plates

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