## 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 language | English (US) |
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Title of host publication | Technical Proceedings of the 2014 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2014 |

Publisher | Nano Science and Technology Institute |

Pages | 77-80 |

Number of pages | 4 |

Volume | 2 |

ISBN (Print) | 9781482258271 |

State | Published - 2014 |

Event | Nanotechnology 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 2014 → Jun 18 2014 |

### Other

Other | Nanotechnology 2014: MEMS, Fluidics, Bio Systems, Medical, Computational and Photonics - 2014 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2014 |
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Country | United States |

City | Washington, DC |

Period | 06/15/14 → 06/18/14 |

## Keywords

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

## ASJC Scopus subject areas

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