Design of electrostatic actuators to tune the effective stiffness of micro-electro-mechanical systems

Micromechanical devices, despite their breadth of application, are frequently based on simple one-degree-of-freedom spring-mass systems. The purpose of the work being presented is to show a method of tuning the behavior of such systems. This tuning ranges from a subtle adjustment of the system's resonant frequency to the formation of multiple potential wells. Specific topics covered include: tuning of the linear stiffness, simulation, independent tuning of the linear and cubic stiffnesses, and formation of multiple potential wells.;We present five electrostatic actuators that tune the stiffness and hence the resonant frequency of a micromechanical oscillator. Using these actuators, resonant frequencies have been reduced to 7.7% and raised to 146% of their original values. These shifts correspond to approximately two orders of magnitude reduction in stiffness and a doubling in stiffness. respectively. Comparisons are drawn based on functionality. area utilization efficiency, and linearity. Discussions include the effects of asymmetries, stability, and nonlinearities.;Associated with the design of tuning actuators is the need to model their behavior. Most of the work is based on a complex electrostatic actuator referred to as a non-overlapping comb drive. This complexity prompted the writing of a 2D electrostatics and elastostatics simulation package referred to as HASP. The package is capable of solving coupled electro-mechanical problems in a self-consistent manner and automatically characterizing an actuator over a line or an array of configurations. With this package, we performed an energy based stability analysis using a computationally efficient strategy. The device under study was a tunable oscillator. By applying a tuning voltage, the effective stiffness of the system was reduced. At a tuning voltage of approximately 50V, a supercritical pitchfork bifurcation was predicted and experimentally verified. Further increase in the tuning voltage was shown to eventually lead to failure.;Frequently micromechanical oscillators and sensors show the presence of cubic stiffness terms in their performance. Using a combination of electrostatic actuators, we present a method to independently tune their linear and nonlinear stiffness coefficients. To demonstrate the methods capability. we investigated the tuning of an oscillator with linear and cubic restoring forces. We successfully tuned the cubic stiffness from ;Finally, the electrostatic tuning actuators are applied to the formation of systems that exhibit multiple potential wells. Using three different tuning actuators, double- and triple-well potentials are demonstrated theoretically and experimentally.