Nonlinear Dynamics of a Micromechanical Torsional Resonator: Analytical Model and Experiments

Mechanical microoscillators have been valuable tools for magnetic measurements of microscopic samples. This paper presents an analytical model for the dynamics of an electrostatically actuated torsional oscillator and validates it experimentally. While, at low excitations, the system is well described by a damped linear oscillator, at higher oscillation amplitudes, a nonlinear regime is observed. Nonlinearity is originated exclusively by the electrostatic driving and detection and can be tuned by modifying the excitation or detection bias voltages. The parameters of the analytical model are obtained from the device dimensions and material properties. No empirical or fitting parameters are needed except for the quality factor, which is extracted from the linear resonance curve. The proposed model can be a valuable and straightforward tool for the design and analysis of many other similar devices based on electrostatically actuated mechanical resonators.