Statistics of power injection in a plate set into chaotic vibration

Olivier Cadot (1) , Arezki Boudaoud (2) , Cyril Touzé (3)

1 DFA - Dynamique des Fluides et Acoustique
2 LPS - Laboratoire de Physique Statistique de l'ENS
3 UME - Unité de Mécanique

A vibrating plate is set into a chaotic state of wave turbulence by either a periodic or a random local forcing. Correlations between the forcing and the local velocity response of the plate at the forcing point are studied. Statistical models with fairly good agreement with the experiments are proposed for each forcing. Both distributions of injected power have a logarithmic cusp for zero power, while the tails are Gaussian for the periodic driving and exponential for the random one. The distributions of injected work over long time intervals are investigated in the framework of the fluctuation theorem, also known as the Gallavotti-Cohen theorem. It appears that the conclusions of the theorem are verified only for the periodic, deterministic forcing. Using independent estimates of the phase space contraction, this result is discussed in the light of available theoretical framework.

Keywords: Fluctuation phenomena; mechanical waves; vibrations; symmetry breaking; Brownian motion; noise; bifurcation; nonlinearity; random processes; elastic waves

Domains: Nonlinear Sciences [physics]; Chaotic Dynamics [nlin.CD]

Olivier Cadot, Arezki Boudaoud, Cyril Touzé. Statistics of power injection in a plate set into chaotic vibration. The European Physical Journal B: Condensed Matter and Complex Systems, 2008, 66 (3), pp.399-407. ⟨10.1140/epjb/e2008-00431-3⟩. ⟨hal-01637690⟩