Journal of Engineering Mathematics

, Volume 53, Issue 3–4, pp 239–252 | Cite as

The effect of the small-aspect-ratio approximation on canonical electrostatic MEMS models

Article

Abstract

The mathematical modeling and analysis of electrostatically actuated micro- and nanoelectromechanical systems (MEMS and NEMS) has typically relied upon simplified electrostatic-field approximations to facilitate the analysis. Usually, the small aspect ratio of typical MEMS and NEMS devices is used to simplify Laplace’s equation. Terms small in this aspect ratio are ignored. Unfortunately, such an approximation is not uniformly valid in the spatial variables. Here, this approximation is revisited and a uniformly valid asymptotic theory for a general “drum shaped” electrostatically actuated device is presented. The structure of the solution set for the standard non-uniformly valid theory is reviewed and new numerical results for several domain shapes presented. The effect of retaining typically ignored terms on the solution set of the standard theory is explored

Keywords

continuation method microelectromechanical systems MEMS nanoelectromechanical systems NEMS nonlinear elliptic problem 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

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