Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

In this study, a homotopy analysis method was used to obtain analytic solutions to predict dynamic pull-in instability of an electrostatically-actuated microbeam. The nonlinear describing equation of a microbeam affected by an electric field including the fringing field effect, based on strain gradient elasticity, couple stress and classical theory was obtained. Influences of different parameters on dynamic pull-in instability were investigated. The equation of motion of a double-clamped microbeam was discretized and solved by using Galerkin’s method via mode summation. The resulting non-linear differential equation was also solved by using the homotopy analysis method (HAM). The influence of HAM parameters on accuracy was studied specifically in the vicinity of the pull-in voltage. Comparison of the results for pull-in voltage indicated at low voltages good agreement existed between numerical and semi-analytical methods while at high voltages HAM results deviated from those of numerical methods. Findings indicate that considering strain gradient and couple stress effects results in a stiffer microbeam than with classical theory. Effects of an auxiliary parameter on convergence were also studied. Convergence domains were determined at different voltages and orders of HAM approximation