Extreme events in a random set of nonlinear elastic bending waves

Abstract

The processes that generate rogue waves on the sea surface remain a mystery. Despite their different natures, the nonlinear bending waves generated in a thin elastic plate share some similarities with waves on the surface of the sea. For instance, both involve four-wave interactions during energy exchange, but in bending waves, the number of waves is not conserved. Here, we present an experimental study to investigate extreme event statistics in random elastic bending waves forced by an electromagnetic shaker on a thin stainless steel plate. In our setup, the standard statistical criterion used to define extreme events, such as rogue waves on the sea surface, is insufficiently restrictive. We therefore apply a new criterion to determine the occurrence frequency of rare events, similar to those observed in wave tanks. With this new criterion, we examine correlations between extreme events amplitude and wave slopes, energy, and periods, raising questions about the links between statistically rare events and rogue waves.