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In this study, a new analytical model is developed for an electrostatic Microelectromechanical System (MEMS) cantilever actuator to establish a relation between the displacement of its tip and the applied voltage. The proposed model defines the micro-cantilever as a rigid beam supported by a hinge at the fixed-end with a spring point force balancing the structure. The approach of the model is based on calculation of the electrostatic pressure centroid on the cantilever beam to localize the equivalent electrostatic point load. Principle outcome of the model is just one formula valid for all displacements ranging from the initial to the pull-in limit position. Our model also shows that the pull-in limit position of a cantilever is approximately 44% of the initial gap. This result agrees well with both simulation results and experimental measurements reported previously. The formula has been validated by comparing the results with former empirical studies. For displacements close to the pull-in limit, the percentage errors of the formula are within 1% when compared with real measurements carried out by previous studies. The formula also gives close results (less than 4%) when compared to simulation outcomes obtained by finite element analysis. In addition, the proposed formula measures up to numerical solutions obtained from several distributed models which demand recursive solutions in structural and electrostatic domains.

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This study presents an inverse approach to obtain a relation between applied voltage and displacement of the midpoint of fixed-fixed beam actuator. The approach has two main sections. The first one is the inverse design of a model to replace real action of upper beam under electrostatic force. The formula obtained from the first section does not comprise the residual stress and gives very small errors when there is no residual stress on the upper electrode. So, the second part was carried out to add this important system variable into the formula. Likewise, inverse solution was again applied in the later section. The final formula demonstrates that pull-in limit of clamped-clamped actuator is to be at around 40% of original spacing that is in agreement with simulation and previous experimental results. Its percentage errors are within 2% when compared with simulations that are based on finite element method (FEM). The results are comparable to numerical solutions received from diverse distributed models which require more calculation power in electrostatic and structural domains. On top of that, our formula is valid for all displacements from original position up to pull-in limit.