Nonlinear micro circular plate analysis using hybrid differential transformation / finite difference method

Cha'O Kuang Chen, Hsin Yi Lai, Chin-Chia Liu

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

Electrostatically-actuated micro circular plates are used in many microelectro- 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.

Original languageEnglish
Pages (from-to)155-174
Number of pages20
JournalCMES - Computer Modeling in Engineering and Sciences
Volume40
Issue number2
Publication statusPublished - 2009 Jan 1

Fingerprint

Circular Plate
Hydrostatic pressure
Finite difference method
Difference Method
Residual stresses
Finite Difference
Hydrostatic Pressure
Optical switches
Electrostatic force
Electric potential
Residual Stress
Micro-electro-mechanical Systems
Nonlinear equations
Equations of motion
Electrostatics
Actuators
Voltage
Pumps
Optical Switch
Electrostatic Force

All Science Journal Classification (ASJC) codes

  • Software
  • Modelling and Simulation
  • Computer Science Applications

Cite this

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abstract = "Electrostatically-actuated micro circular plates are used in many microelectro- 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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Nonlinear micro circular plate analysis using hybrid differential transformation / finite difference method. / Chen, Cha'O Kuang; Lai, Hsin Yi; Liu, Chin-Chia.

In: CMES - Computer Modeling in Engineering and Sciences, Vol. 40, No. 2, 01.01.2009, p. 155-174.

Research output: Contribution to journalArticle

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