Nonlinear dynamics of adhesive micro-spherical particles on vibrating substrates

Abstract

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 a nearly stationary axis tilted with respect to the substrate normal (as opposed to the substrate normal itself). In current study, the leaning angles of the rocking motion with whirling of a set of polystyrene latex particles are approximated by utilizing the coupled dynamic model. Also, the work-of-adhesion values extracted from the experimental resonance frequencies of a set of particles using the developed model are compared to those reported in the literature and a good agreement is found. The detection and analysis of the reported motion is relevant to adhesion bond characterization and particle manipulation.