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Analytic solutions to the oscillatory behavior and primary resonance of electrostatically actuated microbridges

Mojahedi, M ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1142/S0219455411004506
  3. Abstract:
  4. In this paper, the vibration and primary resonance of electrostatically actuated microbridges are investigated, with the effects of electrostatic actuation, axial stress, and mid-plane stretching considered. Galerkin's decomposition method is adopted to convert the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. The homotopy perturbation method (a special case of homotopy analysis method) is then employed to find the analytic expressions for the natural frequencies of predeformed microbridges, by which the effects of the voltage, mid-plane stretching, axial force, and higher mode contribution on the natural frequencies are studied. The primary resonance of the microbridges is also investigated, where the microbridges are predeformed by a DC voltage and driven to vibrate by an AC harmonic voltage. The methods of homotopy perturbation and multiple scales are combined to find the analytic solution for the steady-state motion of the microbeam. In addition, the effects of the design parameters and damping on the dynamic responses are discussed. The results are shown to be in good agreement with the existing ones
  5. Keywords:
  6. MEMS ; NEMS ; Vibration ; AC harmonics ; Analytic expressions ; Analytic solution ; Axial forces ; Axial stress ; DC voltage ; Decomposition methods ; Design parameters ; Galerkin ; Higher mode ; Homotopies ; Homotopy analysis methods ; Homotopy perturbation method ; Micro beams ; Microbridges ; Multiple scale ; Nonlinear ordinary differential equation ; Nonlinear partial differential equations ; Oscillatory behaviors ; Predeformed ; Primary resonance ; Circuit resonance ; Dynamic response ; Electrostatic actuators ; Natural frequencies ; Nonlinear equations ; Ordinary differential equations ; Partial differential equations ; Perturbation techniques ; Vibration analysis
  7. Source: International Journal of Structural Stability and Dynamics ; Volume 11, Issue 6 , December , 2011 , Pages 1119-1137 ; 02194554 (ISSN)
  8. URL: http://www.worldscientific.com/doi/abs/10.1142/S0219455411004506