## Wave turbulence in vibrating plates

The concept of wave turbulence has been introduced about 50 years ago in the context of water waves.

It consists in an asymptotic expansion of the cumulant terms of the dynamics that leads eventually to a kinetic equation.

Beside the thermodynamical equilibrium solutions, this kinetic equation exhibits the so-called Kolmogorov-Zalharov spectra that transport

quantities through the different scales.

We will investigate the dynamics of a vibrating elastic plate in this framework : a Kolmogorov-Zakharov spectrum is predicted which corresponds to a cascade

of energy to small scales. We will then discuss how these results compare with different experiments and will address some explanations for the discrepancy

observed. Finally, we will study the possibility for such a system to present an inverse cascade, something a priori not predicted by the theory.