Abstract. 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 a ected by an electric eld, including the fringing eld e ect, was obtained based on strain gradient elasticity, couple stress, and classical theory. In uences of di erent 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 di erential equation was also solved by using the Homotopy Analysis Method (HAM). The in uence of HAM parameters on accuracy was studied speci cally in the vicinity of the pull-in voltage. Comparison of the results of pull-in voltage indicated that low-voltage good agreement exists between numerical and semi-analytical methods, while HAM results deviated from those of numerical methods at high voltages. Findings indicate that strain gradient and couple stress e ects result in a sti er microbeam than with classical theory. E ects of an auxiliary parameter on convergence were also studied. Convergence domains were determined at di erent voltages and orders of HAM approximation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.