An approach to predicting static responses of electrostatically actuated microbeam under the effect of fringing field and Casimir force

• Analytical approximations to static electromechanical responses of a microbeam are determined.
• The fringing field, Casimir force and axial residual stress are considered.
• The expressions are brief and all parameters appear explicitly.
• Results show excellent agreement with numerical solutions for whole range of beam deflection.

An analytical approximation method is proposed to predict the static response of an axially stressed clamped–clamped microbeam. The beam is subjected to one-sided or symmetric two-sided electrostatic actuations, and the effect of fringing field and Casimir force is also considered. The method is based on the combination of the potential energy formulation and the choice of the form function. Stability analyses of solutions are performed. Analytical approximate solutions have brief expressions. Results are compared with numerical shooting solutions and excellent agreements are observed for whole range of microbeam-center deflection. These expressions can easily be used to derive the effects of various physical parameters on mechanical behavior of electrostatically actuated microbeams.