Experimental and analytical study of highly tunable electrostatically actuated resonant beams

We demonstrate theoretically and experimentally highly tunable clamped-clamped microbeam resonators actuated with electrostatic forces. Theoretically, the Galerkin procedure is used to solve for static deflection as well as the eigenvalue problem as a function of the dc voltage for different values of the ratio between the air gap and the thickness of the microbeam. We demonstrate theoretically and experimentally that the natural frequency of the microbeam can increase or decrease with the increase of the dc polarization voltage depending on the ratio between the air gap and the thickness. Hence, we show that unlike the classical softening effect of the dc voltage, by careful designs of the microbeams, the dc bias can be used to effectively increase the resonance frequencies by several factors. Experimental data are presented for two case studies of silicon beams showing the effective increase of their fundamental resonance frequencies by more than 50-80%. Excellent agreement is reported among the theoretical and experimental results.