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Closed form solutions for the motion of electrically excited micro-cantilever beams

Ghaemi Oskouei, S. B ; Sharif University of Technology | 2006

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  1. Type of Document: Article
  2. DOI: 10.1115/IMECE2006-14964
  3. Publisher: American Society of Mechanical Engineers (ASME) , 2006
  4. Abstract:
  5. The differential equation governing the motion of an electrically excited capacitive microcantilever beam is a nonlinear PDE [1]. Accurate analysis about its motion is of great importance in MEMS' dynamical response. In this paper first the nonlinear 4th order 2 point boundary value problem (ODE) governing the static deflection of the system is solved using three methods. 1. The nonlinear part is linearized and its exact solution is obtained. 2. For low applied DC voltages (not near pull-in) the solutin is found using the direct straight forward perturbation analysis. 3. Numerical computer solutions which are used for the previous solution's verifications. The next parts are devoted to the dynamic solution. The nonlinear time variant 4th order PDE governing the dynamic deflection of an electrically excited microbeam is scrutinized. First using the Galerkin Method the mode shapes and the first three mode temporal equations of the linearized equation are found. Considering no damping, using the perturbations method the temporal equations are solved in three states: far from resonance, near 1:1 resonance and near 1:2 resonance. Finally the damped equation is solved using the aforementioned method. In the literature no closed form solution for this problem is presented. Copyright © 2006 by ASME
  6. Keywords:
  7. Boundary value problems ; Cantilever beams ; Dynamic response ; Electric excitation ; Galerkin methods ; MEMS ; DC voltages ; Linearized equation ; Micro-cantilever beams ; Equations of motion
  8. Source: 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006, Chicago, IL, 5 November 2006 through 10 November 2006 ; 2006 ; 1096665X (ISSN); 0791837904 (ISBN); 9780791837900 (ISBN)
  9. URL: https://asmedigitalcollection.asme.org/IMECE/proceedings-abstract/IMECE2006/47756/379/317452