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In this paper, parametric excitation of a repulsive force electrostatic resonator is studied. A theoretical model is developed and validated by experimental data. A correspondence of the model to Mathieu's Equation is made to prove the existence and location of parametric resonance. The repulsive force creates a combined response that shows parametric and subharmonic resonance when driven at twice its natural frequency. The resonator can achieve large amplitudes of almost 24 m and can remain dynamically stable while tapping on the electrode. Because the pull-in instability is eliminated, the beam bounces off after impact instead of sticking to the electrode. This creates larger, stable trajectories that would not be possible with traditional electrostatic actuation. A large dynamic range is attractive for MEMS resonators that require a large signal-to-noise ratio.

In this study, a linear electrostatic MEMS actuator is introduced. The system consists of a MEMS cantilever beam with combined parallel-plate and electrostatic levitation forces. By using these two forcing methods simultaneously, the static response and natural frequency can be made to vary linearly with voltage. The static response shows a linear increase of 90nm per volt and is maintained for more than 12µm of tip displacement. The natural frequency shows a linear increase of 16Hz per volt and is maintained throughout a 2.9kHz shift in natural frequency. This wide range of linear displacement and frequency tunability is extremely useful for MEMS sensors and actuators, which suffer from the inherent nonlinearity of electrostatic forces. A theoretical model of the system is derived and validated with experimental data. Static, natural frequency, and frequency response calculations are performed. Merging these two mechanisms enables high oscillation branches for a wide range of frequencies with potential applications in MEMS filters, oscillators and sensors.

We demonstrate a tunable air pressure switch. The switch detects when the ambient pressure drops below a threshold value and automatically triggers without the need for any computational overhead to read the pressure or trigger the switch. The switch exploits the significant fluid interaction of a MEMS beam undergoing a large oscillation from electrostatic levitation to detect changes in ambient pressure. If the oscillation amplitude near the resonant frequency is above a threshold level, dynamic pullin is triggered and the switch is closed. The pressure at which the switch closes can be tuned by adjusting the voltage applied to the switch. The use of electrostatic levitation allows the device to be released from their pulledin position and reused many times without mechanical failure. A theoretical model is derived and validated with experimental data. It is experimentally demonstrated that the pressure switching mechanism is feasible.

Parametric resonators that show large amplitude of vibration are highly desired for sensing applications. In this paper, a microelectromechanical system (MEMS) parametric resonator with a flexible support that uses electrostatic fringe fields to achieve resonance is introduced. The resonator shows a 50% increase in amplitude and a 50% decrease in threshold voltage compared with a fixed support cantilever model. The use of electrostatic fringe fields eliminates the risk of pull-in and allows for high amplitudes of vibration. We studied the effect of decreasing boundary stiffness on steady-state amplitude and found that below a threshold chaotic behavior can occur, which was verified by the information dimension of 0.59 and Poincaré maps. Hence, to achieve a large amplitude parametric resonator, the boundary stiffness should be decreased but should not go below a threshold when the chaotic response will appear. The resonator described in this paper uses a crab-leg spring attached to a cantilever beam to allow for both translation and rotation at the support. The presented study is useful in the design of mass sensors using parametric resonance (PR) to achieve large amplitude and signal-to-noise ratio.