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On the Nonlinear Dynamics of a Doubly Clamped Microbeam Near Primary Resonance

[+] Author and Article Information
Nizar R. Jaber

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

Karim M. Masri

Department of Mechanical Engineering,
State University of New York,
Binghamton, NY 13850

Mohammad I. Younis

Physical Science and Engineering Division,
King Abdullah University of Science and Technology (KAUST),
P. O. Box 4700,
Thuwal 23955-6900, Saudi Arabia;
Department of Mechanical Engineering,
State University of New York,
Binghamton, NY 13850
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 25, 2017; published online May 30, 2017. Assoc. Editor: Hanna Cho.

J. Vib. Acoust 139(4), 040902 (May 30, 2017) (5 pages) Paper No: VIB-16-1563; doi: 10.1115/1.4036399 History: Received November 28, 2016; Revised March 25, 2017

This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency–response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of direct current (DC) bias revealing hardening, mixed, and softening behavior of the microbeam. A multimode Galerkin model combined with a shooting technique are implemented to generate the frequency–response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show a good agreement with the experimental data.

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Figures

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Fig. 1

A cross-sectional view of the fabricated microbeam

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Fig. 2

A top view picture of the fabricated microbeam and the actuation pad

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Fig. 3

Experimental setup used for testing the MEMS device

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Fig. 4

Schematic of the doubly clamped microbeam with the half electrode

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Fig. 5

A three-dimensional map of the microstructure profile as seen from the top

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Fig. 6

Static deflection of the beam midpoint with the DC voltage until pull-in

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Fig. 7

Frequency–response to white noise actuation signal at VDC = 30 V, VAC = 50 V, and at 4 mTorr chamber pressure

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Fig. 8

Frequency–response curve showing almost linear behavior at VDC = 20 V and VAC = 5 V

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Fig. 9

Frequency–response curve showing hardening behavior at VDC = 25 V and VAC = 5 V

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Fig. 10

Frequency–response curve showing a hardening then softening behavior (mixed response) at VDC = 35 V and VAC = 5 V

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Fig. 11

Frequency–response curve showing a hardening then softening behavior (mixed response) at VDC = 40 V and VAC = 5 V

Grahic Jump Location
Fig. 12

Frequency–response curve showing a softening behavior at VDC = 45 V and VAC = 5 V

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