Impact on floating membranes
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.
Cite
@article{arxiv.1603.05871,
title = {Impact on floating membranes},
author = {Nicolas Vandenberghe and Laurent Duchemin},
journal= {arXiv preprint arXiv:1603.05871},
year = {2016}
}