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TECHNICAL PAPERS

Open-Loop Nonlinear Vibration Control of Shallow Arches via Perturbation Approach

[+] Author and Article Information
W. Lacarbonara

Dipartimento di Ingegneria Strutturale e Geotecnica, University of Rome La Sapienza, via Eudossiana, 18 Rome 00184, Italy

C.-M. Chin

VSAS Center General Motors Corporation, MC 480-305-200, 6440 E. 12 Mile Rd., Warren, MI 48090-9000

R. R. Soper

Westvaco Covington Research Laboratory, 752 N. Mill Road, Covington, VA 24426

J. Appl. Mech 69(3), 325-334 (May 03, 2002) (10 pages) doi:10.1115/1.1459069 History: Received October 18, 2000; Revised October 25, 2001; Online May 03, 2002
Copyright © 2002 by ASME
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Figures

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Shallow arch geometry with the disturbance and the control input
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First and second-order shape functions: (a) Uc; (b) B; (c) χ1 and χ2; (d) χ3 and χ4; (e) χ5 and χ6; (f ) χ7; (g) χ8; (h) χ9; (i ) χ10; and ( j) χ11 when b=16.5,uB=1.0, and Uc=28.936
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Regions of activation/nonactivation of the principal parametric resonance in the plane of the disturbance frequency detuning and gain when b=16.5 and μ=0.05
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Frequency-response curve of the uncontrolled arch when b=16.5,μ=0.05, and uB=1. Solid (dashed) line indicates stable (unstable) solutions.
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Regions (shaded) of nonactivation of the principal parametric resonance in the plane of the disturbance and control gains for different control phase angles when b=16.5 and μ=0.05
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Uncontrolled (thin line) and optimally controlled (thick line) dynamic deflections at seven discrete times equally spaced within a period of oscillation when b=16.5,μ=0.05,uB=1,σ=−10, and Uc=28.936
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Time histories of the uncontrolled and optimally controlled deflections (ψc=0 and Uc=28.936) at x=1/4 when uB=1,σ=−10,b=16.5,μ=0.05,p(0)=1.5, and q(0)=−0.95
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Time histories of the controlled deflections (second-order solution) at x=1/4 in the detuned case when (a) Δσ=σ−σc=−9.55 and (b) Δσ=8.95 and ψc=0,Uc=28.936,σ=−10,b=16.5,μ=0.05,uB=1,p(0)=1.5, and q(0)=−0.95

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