Synchronized micromechanical resonators with a nonlinear coupling element

Abstract

In this research, the synchronization of 100 nm thick coupled Si resonators is investigated and the mechanical properties of coupling elements are evaluated. Three mechanically coupled resonators with an integer ratio of resonant frequencies are fabricated, and the synchronized condition of these resonators is evaluated by sweeping the frequency of the sinusoidal driving signal. When the synchronization is complete, the entrainment of the resonance occurs, where the frequency ratios become integer and their phase differences are locked by the coupling spring of the support part. Similarly, the driven voltage dependence on the entrainment region, called ‘Arnold's tongue', is observed. The entrainment region is increased as the driving force is increased. Near the resonant frequency of each resonator, a wide entrainment region is observed. This entrainment is caused by the mechanical coupling via the nonlinearity of the support part. By using a simple dynamic model based on a spring–mass system, the nonlinearity of the coupling springs is evaluated from the entrainment region.