Elastic Weak Turbulence: from the vibrating plate to the drum

TL;DR

This study investigates wave turbulence in thin elastic plates under increasing tension, revealing that weak turbulence persists from plates to membranes without transitioning into solitonic regimes or shock formations, supported by theoretical, experimental, and numerical evidence.

Contribution

It demonstrates that weak turbulence theory applies to elastic membranes derived from plates, contrasting with water wave behavior and showing no shock formation in stretched elastic systems.

Findings

Weak turbulence persists across the transition from plates to membranes.

No solitonic or shock regimes are observed in the stretched elastic plates.

Weak turbulence theory remains valid for elastic membranes under tension.

Abstract

Weak wave turbulence has been observed on a thin elastic plate in previous work. Here we report theoretical, experimental and numerical studies of wave turbulence in a thin elastic plate submitted to increasing tension. When increasing the tension (or decreasing the bending stiffness of the plate) the plate evolves progressively from a plate into an elastic membrane as in drums. We start from the plate and increase the tension in experiments and numerical simulations. We observe that the system remains in a state of weak turbulence of weakly dispersive waves. This observation is in contrast with what has been observed in water waves when decreasing the water depth, which also changes the waves from dispersive to weakly dispersive. The weak turbulence observed in the deep water case evolves into a solitonic regime. Here no such transition is observed for the stretched plate. We then apply the weak turbulence theory to the membrane case and show with numerical simulations that indeed the weak turbulence framework remains valid for the membrane and no formation of singular structures (shocks) should be expected in contrast with acoustic wave turbulence.