Analytical model of electrostatic fixed-fixed microbeam for pull-in voltage

The pull-in problem of fixed-fixed beam structures cannot be solved analytically due to its nonlinear from the large deflection and the electrostatic driving force. So to understanding the characters of the devices, the designers have to resort to numerical techniques. Lack of an accurate model for predicting pull-in voltage for basic micromachined beam structures necessitates the clear need for a closed form expression for the pull-in voltage. A new analytical model has been developed based on Rayleigh-Ritz method for determining the pull-in voltage of an electrostatically actuated micro-beam. Three new parameters with the dimension of voltage square have been introduced for considering the contribution from stretch stress gradient non-linear stiffening, bending, and the residual stress. Thus, the model can takes into account the effects of axial stress, residual stress, stretch stress gradient non-linear stiffening, and fringing fields on the pull-in voltage. Modeling result has been compared with published work of other researchers available in the literature and FEM simulation results, it is found the presented model estimation results agree well with FEM simulated results in most common case.