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Research Papers

Statics and Dynamics of MEMS Arches Under Axial Forces

[+] Author and Article Information
Mohammad I. Younis

e-mail: myounis@binghamton.edu
Department of Mechanical Engineering,
State University of New York at Binghamton,
Binghamton, NY 13902

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received April 7, 2012; final manuscript received August 26, 2012; published online February 25, 2013. Assoc. Editor: Steven W. Shaw.

J. Vib. Acoust 135(2), 021007 (Feb 25, 2013) (7 pages) Paper No: VIB-12-1094; doi: 10.1115/1.4023055 History: Received April 07, 2012; Revised August 26, 2012

This works aims to investigate the effect of axial forces on the static behavior and the fundamental natural frequency of electrostatically actuated MEMS arches. The analysis is based on a nonlinear equation of motion of a shallow arch under axial and electrostatic forces. The static equation is solved using a reduced-order model based on the Galerkin procedure. The effects of the axial and electrostatic forces on the static response are examined. Then, the eigenvalue problem of the arch is solved for various equilibrium positions. Several results are shown for the variations of the natural frequency and equilibrium position of the arch under axial forces ranging from compressive loads beyond buckling to tensile loads and for voltage loads starting from small values to large values near the pull-in instability. It is found that the dynamics of MEMS arches are very sensitive to axial forces, which may be induced unintentionally through microfabrication processes or due to temperature variations while in use. On the other hand, it is shown that axial forces can be used deliberately to control the dynamics of MEMS arches to achieve desirable functions, such as extending their stable operation range and tuning their natural frequencies.

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Figures

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Fig. 1

Schematic diagram for electrostatically actuated arch with axial forces

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Fig. 2

The static deflection of the arch under various voltages and nondimensional axial loads. (a) N = 30, VDC = 0 V, (b) N = −30, VDC = 0 V, (c) N = 0, VDC = 30 V, (d) N = 0, VDC = 100 V, and (e) N = 30, VDC = 30 V.

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Fig. 3

The effect of the axial force on the static equilibria of the arch (solid: stable, dashed: unstable). Also shown are schematics for the arch configuration next to the stable solutions.

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Fig. 4

The effect of the axial force on the static equilibria of the arch for VDC = 10 V (solid: stable, dashed: unstable)

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Fig. 5

The effect of the axial force on the static equilibria of the arch for VDC = 100 V (solid: stable, dashed: unstable). Also shown are schematics for the arch configuration next to the stable solutions.

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Fig. 6

The effect of the electrostatic force on the static equilibria of the arch for N = 30 (solid: stable, dashed: unstable). Also shown are schematics for the arch configuration next to the stable solutions.

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Fig. 7

The effect of the electrostatic force on the static equilibria of the arch for N = −30 (solid: stable, dashed: unstable). Also shown are schematics for the arch configuration next to the stable solutions.

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Fig. 8

Variation of the fundamental natural frequency versus the axial load for VDC = 0 V. To convert to dimensional natural frequency in Hz, multiply by 930.3.

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Fig. 9

Variation of the fundamental natural frequency versus the axial load for VDC = 100 V. To convert to dimensional natural frequency in Hz, multiply by 930.3.

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Fig. 10

Variation of the fundamental natural frequency versus the VDC for N = 0. To convert to dimensional natural frequency in Hz, multiply by 930.3.

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Fig. 11

Variation of the fundamental natural frequency versus the VDC for N = 30. To convert to dimensional natural frequency in Hz, multiply by 930.3.

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Fig. 12

Variation of the fundamental natural frequency versus the VDC for N = −30. To convert to dimensional natural frequency in Hz, multiply by 930.3.

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