Highly Tunable Electrothermally and Electrostatically Actuated Resonators

This paper demonstrates experimentally, theoretically, and numerically for the first time, a wide-range tunability of an in-plane clamped-clamped microbeam, bridge, and resonator actuated electrothermally and electrostatically. Using both actuation methods, we demonstrate that a single resonator can be operated at a wide range of frequencies. The microbeam is actuated electrothermally by passing a dc current through it, and electrostatically by applying a dc polarization voltage between the microbeam and the stationary electrode. We show that when increasing the electrothermal voltage, the compressive stress inside the microbeam increases, which leads eventually to its buckling. Before buckling, the fundamental frequency decreases until it drops to very low values, almost to zero. After buckling, the fundamental frequency increases, which is shown to be as high as twice the original resonance frequency. Adding a dc bias changes the qualitative nature of the tunability both before and after buckling, which adds another independent way of tuning. This reduces the dip before buckling, and can eliminate it if desired, and further increases the fundamental frequency after buckling. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared with the experimental data and simulation results of a multi-physics finite-element model. A good agreement is found among all the results.