Frequency Stabilization in a MEMS Oscillator with 1:2 Internal Resonance

One of the most important functionalities of micro-electro-mechanical systems (MEMS) oscillators is to provide a reference frequency with a minimal frequency fluctuation. This paper reports the design and experimental characterization of 1:2 internal resonances (IR) in two distinct (stepped and uniform) doubly clamped micromechanical beam resonators. We have intentionally imposed an IR condition in the initial design of a geometrically nonlinear stepped beam, optimized the geometry using a reliability-based design optimization (RDO), fabricated and characterized the resonance behaviors and modal energy transfer in the response. Strong intermodal coupling through the mechanism of IR in the dynamic response provides the basis to design MEMS oscillators with highly stable reference frequencies. We report that the frequency stabilization can be achieved over a much broader range of operation because of the strong coupling between the two flexural modes.