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

Derakhshan, R ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.24200/sci.2017.4315
  3. Publisher: Sharif University of Technology , 2018
  4. Abstract:
  5. 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, was obtained based on strain gradient elasticity, couple stress, and classical theory. 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 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 effects result 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. © 2018 Sharif University of Technology. All rights reserved
  6. Keywords:
  7. HAM ; Microbeam ; Differential equations ; Electric field effects ; Electric fields ; Electrostatic actuators ; Equations of motion ; Galerkin methods ; Nonlinear equations ; Electrostatically actuated microbeam ; Homotopy analysis methods ; Micro beams ; Nonlinear differential equation ; Pull-in ; Semi-analytical methods ; Strain gradient elasticity ; Strain gradient theory ; Numerical methods
  8. Source: Scientia Iranica ; Volume 25, Issue 1 , 2018 , Pages 175-185 ; 10263098 (ISSN)
  9. URL: http://scientiairanica.sharif.edu/article_4315.html