Effect of external electric potential on the mechanical resonance of MEMS cantilever resonator

This work presents an analytical model to predict the natural frequency of electrostatically actuated micromachined cantilever beam under the application of DC voltage. The analytical modelling uses an energy based method with a sinusoidal vibration assumption. The electric field between the cantilever electrodes is assumed to be vertical and fringing field effects are neglected. The behaviour of natural frequency and a closed-form expression for pull-in voltage are evaluated. The electrostatic spring softening effect of DC bias on the resonant natural frequency is studied in particular. Results are compared with simulation in ANSYS.