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Studying dynamic pull-in behavior of microbeams by means of the homotopy analysis method

Moghimi Zand, M ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1115/IMECE2008-68214
  3. Publisher: 2009
  4. Abstract:
  5. In this study, the homotopy analysis method (HAM) is used to study dynamic pull-in instability in microbeams considering different sources of nonlinearity. Electrostatic actuation, fringing field effect and midplane stretching causes strong nonlinearity in microbeams. In order to investigate dynamic pull-in behavior, using Galerkin's decomposition method, the nonlinear partial differential equation of motion is reduced to a single nonlinear ordinary differential equation. The obtained equation is solved analytically in time domain using HAM. The problem is studied by two separate manners: direct use of HAM and indirect use of HAM in conjunction with He's Modified Lindstedt- Poincaré Method. To demonstrate the effectiveness of the solution methods, results are compared with those in literature. The comparison between obtained results and those available in literature shows good agreement. Copyright © 2008 by ASME
  6. Keywords:
  7. Decomposition methods ; Direct use ; Electrostatic actuation ; Fringing field effects ; Galerkin ; Homotopy analysis methods ; Micro beams ; Non-Linearity ; Nonlinear ordinary differential equation ; Nonlinear partial differential equations ; Poincare ; Pull-in ; Pull-in instability ; Solution methods ; Strong nonlinearity ; Time domain ; Control nonlinearities ; Dynamics ; Electrostatic actuators ; Equations of motion ; Helium ; Mechanical engineering ; Ordinary differential equations ; Partial differential equations ; Dynamic mechanical analysis ; Manufacture ; Nonlinear equations ; Nonlinear equations ; Time domain analysis
  8. Source: 2008 ASME International Mechanical Engineering Congress and Exposition, IMECE 2008, Boston, MA, 31 October 2008 through 6 November 2008 ; Volume 13, Issue PART A , 2009 , Pages 129-135 ; 9780791848746 (ISBN)
  9. URL: https://asmedigitalcollection.asme.org/IMECE/proceedings-abstract/IMECE2008/48746/129/339135