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

Document Type : Article

Authors

1 Sharif University of Technology, School of Mechanical Engineering, Tehran, Iran

2 Sharif University of Technology, School of Mechanical Engineering, Center of Excellence in Design, Robotic and Automation, Tehran, Iran

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

Main Subjects


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