Nonlinear dynamics of adhesive micro-spherical particles on vibrating substrates

The coupled (rocking and out-of-plane) vibrational dynamics of micro-spherical particles on vibrating flat substrates is studied experimentally, analytically, and computationally. In the experimental spectral responses of some of vibrating particles, in addition to their predicted rocking resonance frequencies, extra resonance peaks at the doubles of these predicted frequencies have been previously observed and reported. To understand and explain the rocking resonance frequency doubling effect, a two-dimensional mathematical model describing the coupled dynamics of a micro-spherical particle in the out-of-plane and rocking coordinates is developed and reported. Previously, the doubling effect was leading to ambiguity in adhesion characterization. It is determined that the frequency doubling observed in the spectral domain responses of particles is caused by nonlinear coupling between the out-of-plane and in-plane modes of motion while the particle is experiencing a whirling-like motion taking place around...