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Article

Optimization of the Individual Stiffness and Damping Parameters in Multiple-Tuned-Mass-Damper Systems

[+] Author and Article Information
Lei Zuo, Samir A. Nayfeh

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

J. Vib. Acoust 127(1), 77-83 (Mar 21, 2005) (7 pages) doi:10.1115/1.1855929 History: Received January 04, 2003; Revised December 30, 2003; Online March 21, 2005
Copyright © 2005 by ASME
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Figures

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(a) Configuration of multiple tuned mass dampers for a SDOF primary system and (b) Formulation of the connections in a passive MTMD system as feedback elements
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Block diagram of decentralized control
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Optimal tuning ratios fi of the individual dampers for n=5 (a) and n=100 (b), optimal frequency spacings fi–fi−1 for n=5 (c) and n=100 (d), where μ=5% and ζs=0
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Optimal damping ratios ζi of the individual dampers for n=5 (a) and n=100 (b), optimal damping coefficients ci=ci/(2miωs) for n=5 (c) and n=100 (d), where μ=5% and ζs=0
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Density of mass distribution ρ(ω/ωs): For n=10 (star), for n=100 (dot), Igusa and Xu’s approximation 16 (solid line); for μ=5%, and ζs=0
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Optimal rms displacement of the primary system versus the number of dampers for μ=5%: ζs=0 (solid), ζs=1% (dotted), and ζs=2% (dashed)
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Optimal tuning ratios fi (a) and damping ratios ζi (b) of the individual dampers versus n for μ=5% and ζs=0; the various symbols for each value of n indicate the correspondence between tuning ratios and damping ratios
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Harmonic response of the displacement of the primary system to base excitation with various numbers of dampers for μ=5% and ζs=0:n=0 (dot), n=1 (dash-dot), n=2 (dash), n=5 (thick solid), n=100 (solid)
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The effect of mass distribution for n=2, μ=5%, and ζs=0
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The effect of mass distribution for n=5, μ=5%, and ζs=0
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Optimal rms displacement of the primary system versus the total mass ratio μ for n=1 and ζs=0 (dash-dot), n=1 and ζs=0.01 (dot), n=5 and ζs=0 (solid), n=10 and ζs=0 (dash)
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Optimal tuning ratio (a) and damping ratio (b) of the individual TMDs as a function of the total mass ratio μ for n=5 and ζs=0
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Harmonic response of the displacement of the primary system to base excitation for n=5 and ζs=0: μ=1% (solid), μ=2% (dash), μ=5% (dot), and μ=10% (dash-dot)
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Robustness of MTMD systems to variations in the mass ms (a) and stiffness ks (b) of the primary system for μ=5% and ζs=0:n=1 (dash), n=5 (solid), n=10 (dot), and n=100 (dash-dot)
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Robustness of MTMD systems to variation of the damping ζs of the primary system for μ=5% and ζs=0 nominally: n=1 (dash), n=5 (solid), n=10 (dot), and n=100 (dash-dot)
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Harmonic response of the displacement of the primary system (ζs=0) when ks is changed: n=5 and Δks/ks=0 (thick solid), n=1 and Δks/ks=0 (solid), n=5 and Δks/ks=−0.1 (thick dot), n=1 and Δks/ks=−0.1 (dot), n=5 and Δks/ks=0.1 (thick dash), n=1 and Δks/ks=0 (dash)

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