Analytical solutions of the electrostatically actuated curled beam problem

M. I. Younis*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data in the literature and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.

Original languageEnglish (US)
Title of host publicationTechnical Proceedings of the 2014 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2014
PublisherNano Science and Technology Institute
Pages77-80
Number of pages4
Volume2
ISBN (Print)9781482258271
StatePublished - 2014
EventNanotechnology 2014: MEMS, Fluidics, Bio Systems, Medical, Computational and Photonics - 2014 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2014 - Washington, DC, United States
Duration: Jun 15 2014Jun 18 2014

Other

OtherNanotechnology 2014: MEMS, Fluidics, Bio Systems, Medical, Computational and Photonics - 2014 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2014
CountryUnited States
CityWashington, DC
Period06/15/1406/18/14

Keywords

  • Cantilever
  • Curled
  • Electrostatic
  • Microbeam
  • Pull-in

ASJC Scopus subject areas

  • Hardware and Architecture
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials

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