Application of Homotopy Analysis Method in Dynamic Analysis of a Microbeam

In this study, homotopy analysismethod is used to derive analytic solutions topredict dynamic pull-in instability of anelectrostatically-actuated microbeam. Thenonlinear governing equation of microbeamaffected by an electric field including fringingfield effect, based on strain gradient elasticity,couple stress and classical theory is obtained.Influences of different parameters on dynamicpull-in instability are investigated. Equation ofmotion of double-clamped microbeam isdiscretized and solved by using Galerkin’smethod via mode summation. The resultingnon-linear differential equation is also solvedby using homotopy analysis method (HAM).Influence of HAM parameters on accuracy isstudied. Comparing the results obtained fordifferent theoretical skim indicates at lowvoltages with respect to pull-in voltage, goodagreement exist between numerical and semianalyticalmethods while as voltage increasesHAM results are deviated from that of Runge-Kutta and Finite Element Method-FiniteDifference Method (FEM-FDM). Findingsindicate, considering strain gradient and couplestress theory results in a more stiff microbeamin comparison with classical theory. In thisstudy numerical and analytical software, suchas MATLAB and MAPLE is used.

کلیدواژه ها:

Microbeam ، Pull-in ، Strain Gradient Theory ، MEMS