Experimental and modeling analysis on entrainment condition of submicrometer thick Si micro mechanical resonators with nonlinear coupling element

In this paper, the synchronization of coupled resonators is investigated. Mechanically coupled three resonators are fabricated, and the synchronized condition of these resonators is evaluated. When the frequency of external driving force approaches to the lowest resonant frequency of the coupled resonators, the entrainment of resonance occurred in other resonators, where the frequency ratios become integer and their phase differences are locked. Moreover, the width of the entrainment region is dependent on the amplitude of resonators. Using a basic physical model of the coupled three resonators, we estimated the coupling springs, which show a strong nonlinearity.