Application of HAM in Dynamic Analysis of an Imperfect Microbeam under Effect of Electric Filed

In this study, homotopy analysis method is used to derive analytic solutions to predict dynamic snap and pull-in instability of an electrostatically-actuated imperfect microbeam. The imperfection is expressed by an initially geometric curved. The nonlinear governing equation of microbeam affected by an electric field including fringing field effect, based on strain gradient elasticity theory is obtained. Influences of different parameters on dynamic pull-in instability are investigated. Equation of motion of double-clamped microbeam is discretized and solved by using Galerkin s method via mode summation. The resulting non-linear differential equation is also solved by using homotopy analysis method (HAM). Influence of HAM parameters on accuracy is studied specifically in the vicinity of the snap and pull-in voltages. Comparing the results obtained for different theoretical skim indicates at low voltages with respect to snap voltage, good agreement exist between numerical and semianalytical methods while as voltage increases HAM results are deviated from that of Runge-Kutta Method.