0
TECHNICAL PAPERS

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

[+] Author and Article Information
Lei Zuo

 Abbott Laboratories, Bldg. AP52S, 200 Abbott Park Road, Abbott Park, IL 60064-6212lei.zuo@abbott.com

Samir A. Nayfeh

Department of Mechanical Engineering, Massachusetts Institute of Technology, Room 3-461A, 77 Massachusetts Avenue, Cambridge, MA 02139nayfeh@mit.edu

J. Vib. Acoust 128(1), 56-65 (Apr 01, 2005) (10 pages) doi:10.1115/1.2128639 History: Received June 03, 2003; Revised April 01, 2005

Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

2DOF TMD for one mode of a primary system

Grahic Jump Location
Figure 2

Control formulation of a passive 2DOF TMD

Grahic Jump Location
Figure 3

Block diagram of the primary system and MDOF TMD viewed as a system with decentralized control

Grahic Jump Location
Figure 4

The normalized system H2 norm as a function of ρ∕d with μ=5% for ζs=0 (solid) and for ζs=1% (dashed)

Grahic Jump Location
Figure 5

Two separate SDOF TMDs for one mode of a primary system

Grahic Jump Location
Figure 6

Frequency responses of the H2 optimal TMD system for μ=5% and ζs=0: ρ∕d=0.780 (solid), two separate TMDs (dash), uniform bar supported at two ends (dash-dot), and SDOF TMD (dot)

Grahic Jump Location
Figure 7

(a) Two-DOF TMD with ρ∕d=0 and (b) SDOF TMD

Grahic Jump Location
Figure 8

Normalized system H2 norm versus mass distribution among two SDOF TMDs for μ=5% and ζs=0

Grahic Jump Location
Figure 9

Bode plots of xs(s)∕x0(s) for ρ∕d=0.2, μ=5%, and ζs=0: original system (dot), optimized with nonnegative constraint (dashed), optimized without nonnegative constraint (solid)

Grahic Jump Location
Figure 10

Optimal modal frequencies and damping ratios of the 2DOF TMD subsystem as a function for ρ∕d for μ=5% and ζs=0

Grahic Jump Location
Figure 11

Optimal parameters of the 2DOF TMD versus ρ∕d for μ=5% and ζs=0

Grahic Jump Location
Figure 12

Optimal ratio ρ∕d of the radius of gyration to the connection spacing d versus mass ratio μ for ζs=0

Grahic Jump Location
Figure 13

Optimal H2 norm of xs∕x0 versus the mass ratio for ζs=0: 2DOF TMD with optimal ρ∕d (solid), two separate TMDs (dashed), and SDOF TMD (dotted)

Grahic Jump Location
Figure 14

Parameters of the optimal 2DOF TMD as a function of the mass ratio μ for ζs=0

Grahic Jump Location
Figure 15

Contour map of normalized minimal H2 norm for various values of ρ∕d1 and ρ∕d2 for μ=5% and ζs=0

Grahic Jump Location
Figure 16

Frequency responses of the H2 optimal 2DOF TMD with symmetric and asymmetric connection locations for μ=5% and ζs=0: ρ∕d1=ρ∕d2=0.780 (solid), ρ∕d1=0.010 and ρ∕d2=3.055 (dashed), SDOF TMD (dotted)

Grahic Jump Location
Figure 17

The effect of ρ∕d for H∞ optimal design with μ=5% for ζs=0 (solid) and for ζs=1% (dashed)

Grahic Jump Location
Figure 18

Frequency responses of the H∞ optimal 2DOF TMD design for μ=5% and ζs=0: optimal ρ∕d=0.751 (solid), two separate TMDs (dashed), uniform bar supported at two ends (dashed-dotted), and SDOF TMD (dotted)

Grahic Jump Location
Figure 19

Bode plots of xs(s)∕x0(s) for ρ∕d=0.2, μ=5%, and ζs=0 obtained by H∞ optimization: original system (dotted), optimized with non-negative constraint (dashed line, peak magnitude of 6.071), optimized without nonnegative constraint (solid line, peak magnitude of 3.384)

Grahic Jump Location
Figure 20

Normalized apparent mass F∕(s2mdxs) of various H∞ optimal 2DOF absorbers obtained without parameters constraints: (a) ρ∕d=1, (b) ρ∕d=0.751, and (c) ρ∕d=0.2. The solid lines denote the total apparent mass and the dashed lines denote the contribution of each absorber mode

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In