Theoretical and experimental investigations of the primary and parametric resonances in repulsive force based MEMS actuators

This work demonstrates an efficient approach to excite primary and parametric resonances of a Microelectromechanical system (MEMS) based repulsive force actuator. The electrostatic micro-actuator design consists of a particular arrangement of the actuating electrodes to create a repulsive like force, offering, therefore, a higher traveling range and eliminating pull-in instability. A generalized form of forced Mathieu equation of motion is first formulated and afterward a perturbation analysis, through the Method of Multiple Scales (MMS), is carried out to find an approximate analytical solution of the micro-actuator dynamic response. The steady-state response is subsequently acquired and then compared with experimental results in the vicinity of the microsystem's natural frequency (primary resonance) and then around twice the same frequency (principal parametric resonance). MMS based frequency, force, and transition curves are obtained for both cases with clearly shown distinct regions bordered by lines in which the bifurcation points are well traced. The results show that the parametric excitation actuation can be more efficient, requiring less power as compared to the primary resonance excitation. Moreover, unlike the classical method where the structure is vulnerable to the dynamic pull-in instability, this design provides a larger amplitude of motion while protecting the structure from any dynamic pull-in instability. The ability of this design in exciting both the parametric and primary resonances can be advantageous for several applications ranging from micro-resonator based logic system to memory-based micro-devices. Besides, this study provides an analytical tool for designing MEMS sensors with higher resolutions as the amplitude of the micro-system is no longer restricted to any geometrical limitation.