Nonlinear Dynamics of a Micro-Electro-Mechanical System With Time-Varying Capacitors

[+] Author and Article Information
Albert C. J. Luo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805e-mail: aluo@siue.edu

Fei-Yue Wang

BEI Technologies Inc., 2700 Systron Drive, Concord, CA 94518e-mail: fwang@systron.com

J. Vib. Acoust 126(1), 77-83 (Feb 26, 2004) (7 pages) doi:10.1115/1.1597211 History: Received June 01, 2002; Revised April 01, 2003; Online February 26, 2004
Copyright © 2004 by ASME
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A simplified mechanical model of the MEMS with a time-varying capacitor
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The sketched phase portrait of a non-damped MEMS system without AC excitation. (xie,0)(i=1,2) is for the equilibrium, and (xj,0)(j=1,2,3) is located on the displacement axis for a specified conservative energy.
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The displacement varying with a conservative energy at the zero velocity for various static loading
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Natural frequency varying with conservative energy for specified static loading
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Resonant condition relative to the Q1-term electrical force (upper) and the Q2-term electrical force (lower) through conservative energy and AC frequency for Q0/Q0 max=0.2
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Conditions for appearance and disappearance of the chaotic motion in resonant layers relative to the Q1-term (upper) and the Q2-term (lower) (Q0/Q0 max=0.2)
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The current and voltage on the capacitor in MEMS relative to the oscillation of the (1:1)-resonance based on the Q2-term for Q0/Q0 max=0.2 and Q2/Q0=0.001 and ϖ=1.73 MHz. The initial condition X0≈0.487 μm,Ẋ0=0.
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The current through the capacitor (Q0/Q0 max=0.2 and Q2/Q0=0.01) relative to the (2:1)-resonance motion based on the Q2-term (upper, ϖ≈3.52 MHz,X0≈0.2249 μm,Ẋ0≈6.4127 m/s) and the Q1-term (lower, ϖ≈3.4 MHz,X0≈0.3818 μm,Ẋ0≈−6.589 m/s).
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Chaotic motions in (4:1)-resonant layer relative to the Q1-term for Q0/Q0 max=0.2 and Q2/Q0=0.3, appearance (upper, Ω=3.7503719290) and disappearance (lower, Ω=3.7389823270)




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