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TECHNICAL PAPERS

Inducing Passive Nonlinear Energy Sinks in Vibrating Systems

[+] Author and Article Information
A. F. Vakakis

Division of Mechanics, National Technical University of Athens, P.O. Box 64042, GR-15710 Zografos, Greece e-mail: vakakis@central.ntua.grDepartment of Mechanical and Industrial Engineering*University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL 61801e-mail: avakakis@uiuc.edu

J. Vib. Acoust 123(3), 324-332 (Jan 01, 2001) (9 pages) doi:10.1115/1.1368883 History: Received July 01, 2000; Revised January 01, 2001
Copyright © 2001 by ASME
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References

Figures

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Numerical responses y1(t),y2(t) of system (1b) for, (a) F=1.0, (b) F=1.26, (c) F=1.5; – oscillator 1, [[dashed_line]] oscillator 2 (Gendelman et al., 2000)
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Energy pumping in the system of Fig. 1(b): (a) plot of Δ(t) [O(ε)approximation], t0≅12.5; (b) comparison between numerical simulation, –, and analytical approximation (14) [O(ε)approximation], [[dashed_line]], close to t0
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Absence of energy pumping in the system of Fig. 1(a): (a) plot of Δ(t); (b) motion of the nonlinear attachment y1(t), – approximation (10), [[dashed_line]] numerical simulation
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Energy pumping in the system of Fig. 1(b): (a) plot of Δ(t); (b) motion of the nonlinear attachment y1(t), – approximation (10), [[dashed_line]] numerical simulation
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Energy pumping in the system of Fig. 1(c): (a) plot of Δ(t); (b) motion of the nonlinear attachment y1(t), – approximation (10), [[dashed_line]] numerical simulation
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Onset of energy pumping in system (1b) for F=Fcr=1.2365: (a) plot of Δ(t); (b) motion of the nonlinear attachment y1(t), – approximation (10), [[dashed_line]]  numerical simulation
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Semi-infinite symmetric linear chain with nonlinear attachment at the end
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Absence of energy pumping in the chain with parameters ε=0.1,λ=0.5,C=5.0,d=1.5,ω22=0.9, impulsive excitation on the fourth particle: (a) motion of the nonlinear attachment y1(t); (b) motion of the neighboring linear oscillator y2(t)
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Energy pumping in the chain with parameters ε=0.1,λ=0.5,C=5.0,d=1.5,ω22=0.4, impulsive excitation on the fourth particle: (a) motion of the nonlinear attachment y1(t); (b) motion of the neighboring linear oscillator y2(t)
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Energy pumping in the chain with parameters ε=0.1,λ=0.5,C=5.0,d=3.5,ω22=0.4, impulsive excitation on the fourth particle: (a) motion of the nonlinear attachment y1(t); (b) motion of the neighboring linear oscillator y2(t)
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(a) Comparison of short and long time approximations for ⌊Hp−2(t)+Hp−1(t)⌋,p=4 for the system of Fig. 9; the numerical simulation is also shown; (b) error function Er(t) for the same system determining the transition point t*

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