Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions

In this paper, a closed-form expression for the pull-in voltage of fixed-fixed beams and fixed-free beams is derived starting from the known expression of a simple lumped spring-mass system. The effects of partial electrode configuration, of axial stress, non-linear stiffening, charge re-distribution and fringing fields are all included in the final expression. Further, the results obtained are summarized and validated with other existing empirical and analytical models as well as with finite element simulation results. The model agrees well with finite element simulation results obtained with COVENTORWARE software.