@article { author = {Derakhshan, R. and Ahmadian, M.T. and Firoozbakhsh, K.}, title = {Pull-in criteria of a nonclassical microbeam under electric field using homotopy method}, journal = {Scientia Iranica}, volume = {25}, number = {1}, pages = {175-185}, year = {2018}, publisher = {Sharif University of Technology}, issn = {1026-3098}, eissn = {2345-3605}, doi = {10.24200/sci.2017.4315}, 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 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}, keywords = {Microbeam,Pull-in,Strain Gradient Theory,HAM}, url = {https://scientiairanica.sharif.edu/article_4315.html}, eprint = {https://scientiairanica.sharif.edu/article_4315_12ffb4d064b69a66fb37ecc4721372ef.pdf} }