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Research Papers

Nonlinear Dynamic Behavior Analysis of Microelectrostatic Actuator Based on a Continuous Model Under Electrostatic Loading

[+] Author and Article Information
Cha’o-Kuang Chen1

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.ckchen@mail.ncku.edu.tw

Chin-Chia Liu

Department of Mechanical Engineering, National Chin-Yi University of Technology, Taichung County, Taiwan 411, R.O.C.

Hsin-Yi Lai

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.

1

Corresponding author.

J. Appl. Mech 78(3), 031003 (Feb 01, 2011) (9 pages) doi:10.1115/1.4002003 History: Received June 22, 2009; Revised March 15, 2010; Posted June 17, 2010; Published February 01, 2011; Online February 01, 2011

Analyzing the dynamic behavior of microelectrostatic devices is problematic due to the complexity of the interactions between the electrostatic coupling effect, the fringing field effect, the residual stress, the tensile stress, and the nonlinear electrostatic force. In this study, this problem is resolved by modeling the electrostatic system using a continuous model and solving the resulting governing equation of motion using a hybrid scheme comprising the differential transformation method and the finite difference method. The feasibility of the proposed approach is demonstrated by modeling the dynamic responses of two fixed-fixed microbeams when actuated by a dc voltage. It is shown that the numerical results for the pull-in voltage deviate by no more than 1.74% from those presented in the literature. The hybrid scheme is then applied to examine the nonlinear behavior of one clamped microbeam actuated by a combined dc/ac scheme. The beam displacement is analyzed as a function of both the magnitude and the frequency of the ac voltage. Finally, the actuating conditions, which ensure the stability of the microbeam, are identified by reference to phase portraits and Poincaré maps. Overall, the results presented in this study show that the hybrid differential transformation and finite difference method provides a suitable means of analyzing a wide variety of common electrostatically actuated microstructures.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Simplified model of parallel plate actuator

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Figure 2

Structure of microbeam

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Figure 3

Variation in dimensionless center-point displacement with dc voltage (note that ac voltage is not applied)

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Figure 4

Variation in dimensionless center-point displacement over time for different ac voltages (note that dc voltage=4 V, N¯=8.7, and ω¯=1)

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Figure 5

Variation in dimensionless center-point displacement over time for ac voltages of 1.44 V, 1.45 V, and 1.46 V, respectively (note that dc voltage=4 V, N¯=8.7, and ω¯=1)

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Figure 6

Variation in dimensionless center-point displacement over time for different dimensionless excitation frequencies (note that ac voltage=0.5 V, dc voltage=4 V, and N¯=8.7)

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Figure 7

Variation in transverse deflection of microbeam along microbeam length as function of dimensionless time (note that ac voltage=0.5 V, dc voltage=2.0 V, N¯=8.7, and ω¯=1)

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Figure 8

Phase portraits of dynamic system at ac actuating voltages of (a) Vac=0.1 V, (b) Vac=0.5 V, (c) Vac=1.0 V, and (d) Vac=1.45 V (note that dc voltage=4.0 V, N¯=8.7, and ω¯=1)

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Figure 9

Poincaré maps of dynamic system at ac actuating voltages of (a) Vac=0.1 V, (b) Vac=0.5 V, (c) Vac=1.0 V, and (d) Vac=1.45 V (note that dc voltage=4.0 V, N¯=8.7, and ω¯=1)

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