Duffing Nonlinearity Localization via Extension Energy Confinement in an Elastic Mode Semicircular Beams Resonator

This letter reports a technique to suppress Duffing nonlinearity in silicon micromechanical resonators. A model of nonlinearity localization is established to analyze the confinement of nonlinear extension energy via vibration mode reconfiguration in beams resonators. Through a process of synchronous vibration between curved beams and its suspension beams, the vibration of resonator transits from stretch to elastic modes with the increase of the beam’s curvature. Based on this principle, a microsemicircular beams resonator with double free-ends is introduced. Working on the elastic mode, the semicircular beams resonator shows a weakened instability of amplitude-frequency effect of only 1.3% of that of a conventional double-ended tuning forks resonator. With localized nonlinearity, the semicircular beams resonator can be operated at large vibration amplitude, thus achieving high-power handling performance with good frequency stability.