Static and dynamic behavior of an electrically excited resonant microbeam

We present a nonlinear model of electrically actuated resonators accounting for the electrostatic forcing of the air gap capacitor, the restoring force, and the axial load applied to the microbeam. The boundary-value problem describing the static deflection of the microbeam under the electrostatic loading is solved numerically. The eigenvalue problem describing the vibration of the microbeam around its statically deflected position is solved numerically for the natural frequencies and mode shapes. Comparison of results generated by our model to the experimental results show excellent agreement, thus verifying the model. Our results show that failure to account for mid-plane stretching in the microbeam restoring force leads to an underestimation of the stability limits. They also show that the ratio of the width of the air gap to the microbeam thickness can be tuned to extend the domain of the linear relationship between the DC polarization voltage and the fundamental natural frequency. This fact and the ability of the nonlinear model to predict the natural frequencies accurately for any DC polarization voltage allow designers to use a wider range of DC polarization voltages in resonators.