Open Access

ARTICLE

Nonlinear Micro Circular Plate Analysis Using Hybrid Differential Transformation / Finite Difference Method

by Cha’o-Kuang Chen¹, Hsin-Yi Lai¹, Chin-Chia Liu¹

1 Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan
2 Corresponding author. Tel.: +886-6-2757575 ext.62140; Fax: +886-6-2342081; E-mail:ckchen@mail.ncku.edu.tw

Computer Modeling in Engineering & Sciences 2009, 40(2), 155-174. https://doi.org/10.3970/cmes.2009.040.155

Abstract

Electrostatically-actuated micro circular plates are used in many micro-electro-mechanical systems (MEMS) devices nowadays such as micro pumps and optical switches. However, the dynamic behavior of these circular plates is not easily analyzed using traditional analytic methods due to the complexity of the interactions between the electrostatic coupling effects. Accordingly, this study develops an efficient computational scheme in which the nonlinear governing equation of the coupled electrostatic force acting on the micro circular plate is solved using a hybrid differential transformation / finite difference approximation method. In deriving the dynamic equation of motion of the micro plate, explicit account is taken of both the residual stress within the plate and the uniform hydrostatic pressure acting on its upper surface. It is shown that the pull-in voltage increases with an increasing value of the residual stress, but reduces with an increasing hydrostatic pressure. The predicted values of the pull-in voltage are found to deviate by no more than 1.75% from those presented in the literature. Overall, the results presented in this study demonstrate that the differential transformation / finite difference method provides a computationally efficient and precise means of obtaining detailed insights into the nonlinear behavior of the micro circular plates used in many of today's MEMS-based actuator systems.

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