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Sensors 2008, 8(2), 1048-1069; doi:10.3390/s8021048
Article

Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates

1
,
2,*  and 3
1 Department of Engineering Science & Mechanics, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, USA 2 Department of Mechanical & Aerospace Engineering, Polytechnic University, Brooklyn, NY 11201, USA 3 The Bradley Department of Electrical & Computer Engineering, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, USA
* Author to whom correspondence should be addressed.
Received: 21 December 2007 / Accepted: 14 February 2008 / Published: 15 February 2008
(This article belongs to the Special Issue Modeling, Testing and Reliability Issues in MEMS Engineering)
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Abstract

We study the influence of von Karman nonlinearity, van der Waals force, and a athermal stresses on pull-in instability and small vibrations of electrostatically actuated mi-croplates. We use the Galerkin method to develop a tractable reduced-order model for elec-trostatically actuated clamped rectangular microplates in the presence of van der Waals forcesand thermal stresses. More specifically, we reduce the governing two-dimensional nonlineartransient boundary-value problem to a single nonlinear ordinary differential equation. For thestatic problem, the pull-in voltage and the pull-in displacement are determined by solving apair of nonlinear algebraic equations. The fundamental vibration frequency corresponding toa deflected configuration of the microplate is determined by solving a linear algebraic equa-tion. The proposed reduced-order model allows for accurately estimating the combined effectsof van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflectionprofile with an extremely limited computational effort.
Keywords: Microelectromechanical systems; microplate; van der Waals force; pull-in insta- bility; microsensor Microelectromechanical systems; microplate; van der Waals force; pull-in insta- bility; microsensor
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Batra, R.C.; Porfiri, M.; Spinello, D. Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates. Sensors 2008, 8, 1048-1069.

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