Nonlinear mode coupling in a MEMS resonator

A single micro-electromechanical (MEMS) resonator can be shown to exhibit behaviors unexpected in a simple resonant structure. For small driving forces, the resonator displays typical simple harmonic oscillator response. As the driving force is increased, the resonator shows the slightly more complex, but well understood, Duffing response. Rather unexpected response behavior can appear when the resonator frequency is detuned by nonlinearity to where two oscillatory modes of the resonator begin to interact through nonlinear coupling due to an internal resonance. The paper focuses on how the resonator response changes as the internal resonance is approached in the operating parameter space and how that behavior is conveniently represented in a bifurcation diagram. This behavior is accurately captured by a generic mathematical model. We describe an analysis of the model which shows how this coupled response varies with the system and drive parameters, especially focusing on the nonlinear coupling strength between the two modes.