## Abstract

We consider the von Kármán nonlinearity and the Casimir force to develop reduced-order models for prestressed clamped rectangular and circular electrostatically actuated microplates. Reduced-order models are derived by taking flexural vibration mode shapes as basis functions for the transverse displacement. The in-plane displacement vector is decomposed as the sum of displacements for irrotational and isochoric waves in a two-dimensional medium. Each of these two displacement vector fields satisfies an eigenvalue problem analogous to that of transverse vibrations of a linear elastic membrane. Basis functions for the transverse and the in-plane displacements are related by using the nonlinear equation governing the plate in-plane motion. The reduced-order model is derived from the equation yielding the transverse deflection of a point. For static deformations of a plate, the pull-in parameters are found by using the displacement iteration pull-in extraction method. Reduced-order models are also used to study linear vibrations about a predeformed configuration. It is found that 9 basis functions for a rectangular plate give a converged solution, while 3 basis functions give pull-in parameters with an error of at most 4%. For a circular plate, 3 basis functions give a converged solution while the pull-in parameters computed with 2 basis functions have an error of at most 3%. The value of the Casimir force at the onset of pull-in instability is used to compute device size that can be safely fabricated.

Original language | English (US) |
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Pages (from-to) | 3558-3583 |

Number of pages | 26 |

Journal | International Journal of Solids and Structures |

Volume | 45 |

Issue number | 11-12 |

DOIs | |

State | Published - Jun 15 2008 |

## Keywords

- Casimir force
- Clamped microelectromechanical plates
- Frequencies
- Reduced-order nonlinear models
- von Kármán nonlinearity

## ASJC Scopus subject areas

- Modeling and Simulation
- General Materials Science
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics