Extreme events in a random set of nonlinear elastic bending waves

We present an experimental setup designed to investigate the statistical properties of extreme events in random elastic bending waves induced by an electromagnetic shaker on a thin stainless steel plate. In this setup, the standard statistical criteria used to define extreme events, such as rogue waves in the sea, are not sufficiently restrictive. Therefore, we introduce a new, more restrictive criterion to quantify the occurrence of rare events, similar to those observed in wave tanks [G. Michel et al., J. Fluid Mech. 943, A26 (2022)10.1017/jfm.2022.436]. Using this refined criterion, we explore correlations between the amplitude of extreme events and other wave characteristics, such as slopes, energy, and periods of the waves. We find that extreme events in our setup are correlated to the longest wavelength of the plate, which corresponds to the plate's mode. We also observe that the steepness and kinetic energy of these events reach their time-averaged value, as expected for these slow-varying modes of the plate. The study raises questions about the purely statistical characterization of statistically rare events and rogue waves.