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Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / Dynamical Systems

J. Math. Phys. 53, 022703 (2012); http://dx.doi.org/10.1063/1.3684748 (13 pages)

Dynamics of electrostatic microelectromechanical systems actuators

Yisong Yang1, Ruifeng Zhang2, and Le Zhao3

1Department of Mathematics, Polytechnic Institute of New York University, Brooklyn, New York 11201, USA
2Institute of Contemporary Mathematics and School of Mathematics, Henan University, Kaifeng, Henan 475004, People's Republic of China
3School of Mathematics, Henan University, Kaifeng, Henan 475004, People's Republic of China

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(Received 5 October 2011; accepted 13 January 2012; published online 13 February 2012)

Electrostatic actuators are simple but important switching devices for microelectromechanical systems applications. Due to the difficulties associated with the electrostatic nonlinearity, precise mathematical description is often hard to obtain for the dynamics of these actuators. Here we present two sharp theorems concerning the dynamics of an undamped electrostatic actuator with one-degree of freedom, subject to linear and nonlinear elastic forces, respectively. We prove that both situations are characterized by the onset of one-stagnation-point periodic response below a well-defined pull-in voltage and a finite-time touch-down or collapse of the actuator above this pull-in voltage. In the linear-force situation, the stagnation level, pull-in voltage, and pull-in coordinate of the movable electrode may all be determined explicitly, following the recent work of Leus and Elata based on numerics. Furthermore, in the nonlinear-force situation, the stagnation level, pull-in voltage, and pull-in coordinate may be described completely in terms of the electrostatic and mechanical parameters of the model so that they approach those in the linear-force situation monotonically in the zero nonlinear-force limit.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. PHYSICAL MODEL AND GOVERNING EQUATION
  3. USE OF THE FIRST INTEGRAL
  4. PERIODIC SOLUTIONS
  5. NON-PERIODIC OR TOUCH-DOWN SOLUTION
  6. A PRECISE DYNAMIC RESPONSE THEOREM
  7. A NONLINEAR ELASTIC FORCE SITUATION
  8. TOUCH-DOWN AS A UNIVERSAL DYNAMICAL PROPERTY

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KEYWORDS, PACS, and IPC

Keywords

elasticity, electrostatic actuators, microswitches

PACS

  • 07.10.Cm

    Micromechanical devices and systems

  • 84.32.Dd

    Connectors, relays, and switches

  • 85.85.+j

    Micro- and nano-electromechanical systems (MEMS/NEMS) and devices

International Patent Classification (IPC)

  • H01H

    Electric switches; Relays; Selectors; Emergency protective devices

  • B81B

    Micro-structural devices or systems, e.g. micro-mechanical devices

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3684748

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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