Impact of a rigid sphere onto an elastic membrane

TL;DR

This paper presents a combined theoretical and experimental study of a rigid sphere impacting an elastic membrane, revealing new phenomena in contact mechanics and validating a detailed predictive model.

Contribution

It introduces a first-principles model for sphere-membrane impact, including contact surface dynamics, validated by experiments, and uncovers novel behaviors like multiple contacts and energy recovery.

Findings

Validated model predicts sphere trajectory and membrane deflection.

Discovered multiple contact phenomena during rebound.

Identified energy recovery effects at low impact velocities.

Abstract

We study the axisymmetric impact of a rigid sphere onto an elastic membrane theoretically and experimentally. We derive governing equations from first principles and impose natural kinematic and geometric constraints for the coupled motion of the sphere and the membrane during contact. The free-boundary problem of finding the contact surface, over which forces caused by the collision act, is solved by an iterative method. This results in a model that produces detailed predictions of the trajectory of the sphere, the deflection of the membrane, and the pressure distribution during contact. Our model predictions are validated against our direct experimental measurements. Moreover, we identify new phenomena regarding the behaviour of the coefficient of restitution for low impact velocities, the possibility of multiple contacts during a single rebound, and energy recovery on subsequent bounces. Insight obtained from this model problem in contact mechanics can inform ongoing efforts towards the development of predictive models for contact problems that arise naturally in multiple engineering applications.