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
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Conference papers
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Thomas Humbert, C Josserand, Cyril Touzé, Olivier Cadot. A phenomenological model for predicting the effect of damping on wave turbulence spectra in vibrating plates. 6th International Conference on Nonlinear Vibrations, Localization and Energy Transfer, Aug 2016, Liège, Belgium. ⟨hal-01354764⟩

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