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An Experimental and Theoretical Investigation of the Mechanical Behavior of Multilayer Initially Curved Microplates Under Electrostatic Actuation

[+] Author and Article Information
S. Saghir

Physical Science and Engineering Division,
King Abdullah University of Science
and Technology (KAUST),
P. O. Box 4700,
Thuwal 23955-6900, Saudi Arabia;
Mechanical Engineering Department,
University of Management and
Technology (UMT),
Daska Road,
Sialkot 51310, Pakistan

S. Ilyas, N. Jaber

Physical Science and Engineering Division,
King Abdullah University of Science
and Technology (KAUST),
P. O. Box 4700,
Thuwal 23955-6900, Saudi Arabia

M. I. Younis

Physical Science and Engineering Division,
King Abdullah University of Science
and Technology (KAUST),
P. O. Box 4700,
Thuwal 23955-6900, Saudi Arabia
e-mail: mohammad.younis@kaust.edu.sa

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 28, 2016; final manuscript received March 14, 2017; published online May 30, 2017. Assoc. Editor: Slava Krylov.

J. Vib. Acoust 139(4), 040901 (May 30, 2017) (11 pages) Paper No: VIB-16-1562; doi: 10.1115/1.4036398 History: Received November 28, 2016; Revised March 14, 2017

We investigate the static and dynamic behavior of a multilayer clamped-free–clamped-free (CFCF) microplate, which is made of polyimide, gold, chromium, and nickel. The microplate is slightly curved away from a stationary electrode and is electrostatically actuated. The free and forced vibrations of the microplate are examined. First, we experimentally investigate the variation of the first natural frequency under the electrostatic direct current (DC) load. Then, the forced dynamic behavior is investigated by applying a harmonic alternating current (AC) voltage superimposed to a DC voltage. Results are shown demonstrating the transition of the dynamic response of the microplate from hardening to softening as the DC voltage is changed as well the dynamic pull-in phenomenon. For the theoretical model, we adopt a dynamic analog of the von Karman governing equations accounting for initial curvature imperfection. These equations are then used to develop a reduced-order model (ROM) based on the Galerkin procedure to simulate the mechanical behavior of the microplate. We compare the theoretical results with the experimental data and show excellent agreement among the results. We also examine the effect of the initial rise on the natural frequencies of first three symmetric–symmetric modes of the plate.

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Figures

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Fig. 1

A schematic diagram of an initially curved CFCF microplate under electrostatic actuation

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Fig. 2

A schematic diagram of a cross section of the fabricated microplate, showing the material layers

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Fig. 3

(a) Three-dimensional micrograph constructed by optical profilometer and (b) top view picture taken under the microscope

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Fig. 4

(a) Curvature profile of the microplate along the length at the center and (b) curvature profile of the microplate along the width at the center

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Fig. 5

Experimental setup showing the microsystem analyzer MSA-500, a vacuum chamber, and data acquisition system

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Fig. 6

First four resonance frequencies and modes of vibration of the microplate, captured when excited by a white noise signal of Vdc = 3 V and Vac = 10 V

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Fig. 7

(a) Linear response at first resonance when actuated by white noise at various values of direct current (DC) load and (b) variation of the first resonance frequency with the DC load

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Fig. 8

Linear and nonlinear responses of the microplate when actuated by various harmonic alternating current (AC) loads superimposed to a constant DC load of 2 V with a step size of 10 Hz and a chamber pressure of 2.6 mTorr

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Fig. 9

Dynamic pull-in when the microplate is actuated by a Vac = 3 V and a Vdc = 2 V with a step size of 1 Hz and a chamber pressure of 2.1 mTorr

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Fig. 10

Frequency response curves near the primary resonance at various DC loads, while an AC load was fixed at 0.5 V, depicting the softening behavior at high DC loads. The step size was 10 Hz, and the chamber pressure was 2.6 mTorr.

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Fig. 11

Forward and backward frequency sweep curves at a Vac = 0.5 V and a Vdc = 12 V. The chamber pressure was fixed at 1.8 mTorr.

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Fig. 12

Initial curvature imperfection profiles at the center of the microplate; experimentally measured “blue line” and approximated “red line,” (a) along the length and (b) along the width (see color figure online)

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Fig. 13

Frequency response plots of the microplate; theory “+” and the experiment “*,” when actuated by a Vac = 1 V and Vdc = 2 V. A quality factor Q = 480 was used for simulation.

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Fig. 14

Frequency response plots of the microplate; theory “+” and the experiment “*,” when actuated by a Vac = 3 V and Vdc = 2 V. A quality factor Q = 480 was used for simulation.

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Fig. 15

Variation of the natural frequency of the symmetric–symmetric modes of vibration with the maximum initial rise of the curvature imperfection: (a) first symmetric–symmetric mode, (b) second symmetric–symmetric mode, and (c) third symmetric-symmetric mode

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