Modeling polygonal oscillations in a liquid drop

Liquid drops when subjected to external periodic perturbations can execute polygonal oscillations. In this work, a simplistic model to simulate these oscillations in the drops is presented. The model consists of a spring-mass network such that the masses represent liquid molecules and the springs are analogous to intermolecular forces. Neo-Hookean springs are considered to model these intermolecular forces. The restoring force of a neo-Hookean spring depends nonlinearly on its length such that the force of a compressed spring is much higher than the force of a spring elongated by the same amount. This is equivalent to the compressible property of incompressible liquids, making these springs suitable to simulate liquid drops. It is shown that the spring-mass network executes polygonal oscillations, the frequencies of polygonal oscillations and perturbation are related by integer or irrational multiples and that the shape of the polygons depends on the parameters of perturbation.