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TECHNICAL PAPERS

# Frequency Analysis of the Tuned Mass Damper

[+] Author and Article Information
Steen Krenk

Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark

J. Appl. Mech 72(6), 936-942 (May 15, 2005) (7 pages) doi:10.1115/1.2062867 History: Received November 05, 2004; Revised May 15, 2005

## Abstract

The damping properties of the viscous tuned mass damper are characterized by dynamic amplification analysis as well as identification of the locus of the complex natural frequencies. Optimal damping is identified by a combined analysis of the dynamic amplification of the motion of the structural mass as well as the relative motion of the damper mass. The resulting optimal damper parameter is about 15% higher than the classic value, and results in improved properties for the motion of the damper mass. The free vibration properties are characterized by analyzing the locus of the natural frequencies in the complex plane. It is demonstrated that for optimal frequency tuning the damping ratio of both vibration modes are equal and approximately half the damping ratio of the applied damper, when the damping is below a critical value corresponding to a bifurcation point. This limiting value corresponds to maximum modal damping and serves as an upper limit for damping to be applied in practice.

###### FIGURES IN THIS ARTICLE
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Copyright © 2005 by American Society of Mechanical Engineers
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## Figures

Figure 7

Locus of modal frequencies, μ=0.05 and ωd∕ω0=(1+μ)−1

Figure 8

Locus of modal frequencies, μ=0.05 and ωd∕ω0=(1+μ)−1

Figure 1

Tuned mass damper

Figure 2

Dynamic amplification for μ=0.05, ωd=ω0 and ζ: (⋯) 0, (—) 0.1, (-∙-) 0.3, (---) ∞

Figure 3

Dynamic amplification of structural mass for μ=0.05 and damping parameter: (---) ζclassic, (—) ζopt, (-∙-) ζ*

Figure 4

Amplitude of relative damper motion μ=0.05 and damping parameter: (---) ζclassic, (—) ζopt, (-∙-) ζ*

Figure 5

Locus of modal frequencies, μ=0.05 and ωd∕ω0=0.94

Figure 6

Locus of modal frequencies, μ=0.05 and ωd∕ω0=0.98

## Errata

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