Formation of Chladni Patterns by Vibration Driven Random Walk of Particles

Abstract

Bouncing of sand particles on a vibrating membrane of a Chladni experiment is characterized statistically. Analysis of recorded particle trajectories reveals that bounces are circularly distributed and random. Their mean horizontal displacement is approximately proportional to the vibration amplitude above the critical level and about one fourth of the jump height. For the description of particle horizontal drifting a new model of vibration driven random walk is developed. Typical examples of Chladni patterns generated numerically by vibration driven random walk reveal a good agreement between simulated and experimentally observed properties.