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TECHNICAL PAPERS

Extending Den Hartog’s Vibration Absorber Technique to Multi-Degree-of-Freedom Systems

[+] Author and Article Information
Mehmet Bulent Ozer

Dept. of Mechanical-Engineering, University of Illinois at Chicago, 2039 Engineering Research Facility, Chicago, IL 60607

Thomas J. Royston1

Dept. of Mechanical-Engineering, University of Illinois at Chicago, 2039 Engineering Research Facility, Chicago, IL 60607troyston@uic.edu

1

Corresponding author.

J. Vib. Acoust 127(4), 341-350 (Oct 26, 2004) (10 pages) doi:10.1115/1.1924642 History: Received January 16, 2004; Revised October 26, 2004

The most common method to design tuned dynamic vibration absorbers is still that of Den Hartog, based on the principle of invariant points. However, this method is optimal only when attaching the absorber to a single-degree-of-freedom undamped main system. In the present paper, an extension of the classical Den Hartog approach to a multi-degree-of-freedom undamped main system is presented. The Sherman-Morrison matrix inversion theorem is used to obtain an expression that leads to invariant points for a multi-degree-of-freedom undamped main system. Using this expression, an analytical solution for the optimal damper value of the absorber is derived. Also, the effect of location of the absorber in the multi-degree-of-freedom system and the effect of the absorber on neighboring modes are discussed.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

MDOF main system and the absorber system

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Figure 2

The two invariant point locations

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Figure 3

The 4-DOF main system used in the case studies

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Figure 4

Undamped response of mass 1

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Figure 5

Response of the first mass when the absorber is attached to the third mass. The absorber parameter calculation method is _ extended Den Hartog method for MDOF systems, ka=10,319N∕m, ca=19.2Ns∕m; _ _ _ _ extended Den Hartog method for MDOF systems with alternative damping calculation method, ka=10,319N∕m, ca=22.0Ns∕m; — — —Den Hartog method applied via modal domain, ka=8129N∕m, ca=25.0Ns∕m.

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Figure 6

Response of the target mass around the third mode when it is attached to different coordinates. The absorber is attached to _ mass 1, ---- mass 2, _ _ _ mass 3, and __ _ __ mass # 4.

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Figure 7

Response of the target mass around the first mode when it is attached to different coordinates. The absorber is attached to _ _ _ mass 1,___ mass 2, ---- mass # 3, — – — – mass # 4.

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Figure 8

Mode-shape drawings of the main system modes

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Figure 9

Optimal response of the system around the third and fourth modes when the absorber is attached to — mass 3 and ----- mass 4

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