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

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.
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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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