Doubling of rocking resonance frequency of an adhesive microparticle vibrating on a surface

For some spherical micro-particles on a vibrating flat substrate, in addition to their predicted rocking resonance frequencies, other resonance peaks at their doubles are observed. Here, a mathematical model and experimental results are presented for explaining this observation. It is determined that the frequency doubling is caused by nonlinear coupling between the out-of-plane and rocking modes of motion, and whirling-like motion that must be present for the presence of doubling effect. It is also found that the work-of-adhesion values extracted from the experimental resonance frequencies of a set of particles using the developed model are in good agreement with those reported in the literature.