An analytical approximation method for predicting static responses of electrostatically actuated microbeams

• Analytical approximations to static electromechanical responses of a microbeam are determined.
• 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 subjected to one-sided and two-sided symmetric electrostatic actuations. The method is based on the combination of the potential energy formulation and the choice of the form function. Stability analyses of solutions can also been 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 microbeams, and to measure residual stress and elastic modulus of material in them.