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RESEARCH PAPERS

Simulation of Squeeze-Film Damping of Microplates Actuated by Large Electrostatic Load

[+] Author and Article Information

Mechanical Engineering Department, State University of New York at Binghamton, Binghamton, NY 13902

Ali H. Nayfeh

Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061anayfeh@vt.edu

J. Comput. Nonlinear Dynam 2(3), 232-241 (Jan 07, 2007) (10 pages) doi:10.1115/1.2727491 History: Received July 12, 2006; Revised January 07, 2007

Abstract

We present a new method for simulating squeeze-film damping of microplates actuated by large electrostatic loads. The method enables the prediction of the quality factors of microplates under a limited range of gas pressures and applied electrostatic loads up to the pull-in instability. The method utilizes the nonlinear Euler-Bernoulli beam equation, the von Kármán plate equations, and the compressible Reynolds equation. The static deflection of the microplate is calculated using the beam model. Analytical expressions are derived for the pressure distribution in terms of the plate mode shapes around the deflected position using perturbation techniques. The static deflection and the analytical expressions are substituted into the plate equations, which are solved using a finite-element method. Several results are presented showing the effect of the pressure and the electrostatic force on the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors.

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Figures

Figure 7

Variation of the quality factor with Vp for Pa=0.01mbar (circles), Pa=1mbar (squares), and Pa=10mbar (stars)

Figure 6

Variation of the calculated ω1i and ω1r with Vp for Pa=0.01mbar (circles), Pa=1mbar (squares), and Pa=10mbar (stars)

Figure 2

Electrically actuated microplate

Figure 1

A schematic of the proposed approach for simulating microplates under the coupled effect of electrostatic, fluidic, and mechanical forces

Figure 8

The spatial variation of the microplate modeshape W1r as a function of pressure and electrostatic load. Data shown in discrete points correspond to Vp=6V and the solid and dashed lines correspond to Vp=28V. The data shown in circles and dashed lines correspond to Pa=0.01mbar and the data in stars and solid lines correspond to Pa=2mbar.

Figure 9

Spatial variation of the pressure distribution underneath the microplate P1r when Vp=6V (discrete points) and Vp=28V (solid and dashed lines). The data shown in circles and dashed lines correspond to Pa=0.01mbar and the data in stars and solid lines correspond to Pa=2mbar.

Figure 5

A comparison of the quality factor and natural frequency of a 210μm length microplate calculated using the present method (circles) and the linearized plate model (2) around the undeflected position (stars) for various values of the dc voltage

Figure 4

A comparison of the natural frequency and quality factor of a microplate calculated using the present method (stars) with those obtained using the finite-element software ANSYS (triangles) for various values of the dc voltage

Figure 3

A comparison of the normalized fundamental natural frequencies of a microplate calculated using the 2-D finite-element model (circles) with those obtained experimentally (stars) (13) and those obtained using a beam model (squares) (8)

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