Frequency-amplitude behavior in the incipient movement of grains under vibration

The onset of the movement of particles placed on a horizontal rough surface subject to a vertical sinusoidal vibration is investigated through tracking experiments,theoretical analysis,and numerical simulations. The frequency of vibration needed to move particles decays exponentially with the amplitude of the oscillatory input.This behavior is explained through a simple mechanism in which a forced damped harmonic oscillator with a spring constant represents all the interactions between the particle and the surface.The numerical results compare well with experimental data,demonstrating that the forces included in the numerical calculations suitably account for the main particle response,even though the complexity of the surface is not fully taken into account.Describing the way in which frequency varies with amplitude could be relevant to technological applications such as cleaning of material surfaces.