An Experimental and Theoretical Investigation of Dynamic Pull-In in MEMS Resonators Actuated Electrostatically

We present experimental and theoretical investigations of dynamic pull-in of electrostatically actuated resonators. Several experimental data are presented, showing regimes of ac forcing amplitude versus ac frequency, where a resonator is forced to pull in if operated within these regimes. Results are shown for primary and secondary resonance excitations. The influences of the initial conditions of the system, the ac excitation amplitude, the ac frequency, the excitation type, and the sweeping type are investigated. A shooting technique to find periodic motions and a basin-of-attraction analysis are used to predict the limits of the pull-in bands. When compared with the experimental data, the results have shown that the pull-in limits coincide with 30%-40% erosion lines of the safe basin in the case of primary resonance and 5%-15% erosion lines of the safe basin in the case of subharmonic resonance. Bifurcation diagrams have been constructed, which designers can use to establish factors of safety to reliably operate microelectromechanical-systems resonators away from pull-in bands and the danger of pull-in, depending on the expected disturbances and noise in the systems.