The dynamics of a membrane shock-absorber

A common means to reduce the impact between two heavy colliding bodies is to interpose between them some sort of elastic buffer that can convert the kinetic energy of the heavy bodies into stored elastic energy. A device of this kind is called a shock absorber. In harbors, for example, bumpers are hung along pier walls or the hull of a ship in order to avoid direct impact during docking. These bumpers are often large pressurized rubber cylinders, that is, pressurized cylindrical elastic membranes. We here describe their dynamical behavior during impact and, in particular, compute the time it takes for the motion to stop after impact.