Universal Resonant and Pull-in Characteristics of Tunable-Gap Electromechanical Actuators

Performance characteristics of tunable-gap electromechanical actuators depend on the complex interaction of forcing function (voltage versus charge actuation), restoring force (linear versus nonlinear spring), and electrode geometry (planar versus nanostructured electrodes); and have been studied on a case-by-case basis. In this paper, we unify the performance characteristics of electromechanical actuators through scaling relationships for pull-in (PI) instability, PI voltage/charge, and resonance frequency. These scaling relationships depend only on two scaling parameters, n and p, related to the electrostatic force and the nature of spring, respectively. This scaling theory not only explains a broad range of experimental data within a single theoretical framework, but can also be used to characterize electrode geometry and nature of spring for any new actuator. The scaling relationships should enable the design of electrode geometry, actuation mechanism, and/or spring for desired performance.