Pull-in voltage analysis for an electrostatically actuated extensional microbeam with large deflection

摘要

This paper presents an analysis of pull-in behavior for nonlinear microelectromechanical coupled microbeams. Based on the accurate geometrically nonlinear theory of Euler-Bernoulli beams, a distributed electromechanical model that accounts for electrostatic fringing field, finite deformation, and residual stress, is proposed. The governing differential equations, in conjunction with the corresponding boundary conditions, constitute a nonlinear two-point boundary value problem which is solved numerically by shooting method. Taking the applied voltage as an unknown and the maximum deflection as a control parameter, the characteristic relations of applied voltage vs. deflection are successfully obtained. In order to confirm the model results, several case studies are compared with available published simulations, showing a good reliability. The influences of various parameters, such as the initial gap-length ratio, fringing field effect, residual stress, on the pull-in parameters have been studied with this method. Numerical results show that the proposed method is accurate and stable, which is an effective method to analyze the deformation of a microbeam.