Impact on floating membranes

TL;DR

This paper investigates the wave dynamics and buckling instability of a floating elastic membrane impacted by a rigid object, revealing similarities to capillary waves with impact-dependent surface tension.

Contribution

It introduces a detailed analysis of impact-induced wave propagation and buckling in floating membranes, highlighting the influence of membrane stretching on wave behavior and instability development.

Findings

Longitudinal wave propagates at constant speed, creating a stress-free domain.

Dispersive transverse waves depend on local stretching rate.

Impact speed influences effective surface tension and wave dynamics.

Abstract

When impacted by a rigid object, a thin elastic membrane with negligible bending rigidity floating on a liquid pool deforms. Two axisymmetric waves radiating from the impact point propagate. In the first place, a longitudinal wave front -- associated with in-plane deformation of the membrane and traveling at constant speed -- separates an outward stress free domain with a stretched but flat domain. Then, in the stretched domain a dispersive transverse wave travels at a wave speed that depends on the local stretching rate. We study the dynamics of this fluid-body system and we show that the wave dynamics is similar to the capillary waves that propagate at a liquid-gas interface but with a surface tension coefficient that depends on impact speed. We emphasize the role of the stretching in the membrane in the wave dynamics but also in the development of a buckling instability that give rise to radial wrinkles.