A general closed-form solution for the static pull-in voltages of electrostatically actuated MEMS/NEMS

In this article, an analytical method for calculating pull-in voltage is proposed. This method can accurately predict pull-in voltage of clamped-free, clamped-clamped and curved micro- and nano-beams. In this study, mid-plane stretching, axial stress, initial deformation and the effect of size are taken into account. To achieve this goal, governing equation of beam based on modified couple stress theory was first derived and then transformed to a single degree of freedom (D.O.F) model by Galerkin method. In this model, electrostatic force appears in integral form which is approximated to non-integral form employing Genetic Algorithm. This single degree of freedom model provides means for obtaining critical deflection of beam and is used to find the general closed-form expression for pull-in voltage. The validation of the method was carried out by comparing the results with the existing literature.