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Technical Brief

Damping of Torsional Beam Vibrations by Control of Warping Displacement

[+] Author and Article Information
Jan Høgsberg

Department of Mechanical Engineering,
Technical University of Denmark,
Kongens Lyngby DK-2800, Denmark
e-mail: jhg@mek.dtu.dk

David Hoffmeyer, Christian Ejlersen

Rambøll,
Hannemanns Alle 53,
Copenhagen DK-2300, Denmark

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 11, 2013; final manuscript received September 16, 2015; published online October 26, 2015. Editor: I. Y. (Steve) Shen.

J. Vib. Acoust 138(1), 014501 (Oct 26, 2015) (5 pages) Paper No: VIB-13-1396; doi: 10.1115/1.4031616 History: Received November 11, 2013; Revised September 16, 2015

Supplemental damping of torsional beam vibrations is considered by viscous bimoments acting on the axial warping displacement at the beam supports. The concept is illustrated by solving the governing eigenvalue problem for various support configurations with the applied bimoments represented as viscous boundary conditions. It is demonstrated that properly calibrated viscous bimoments introduce a significant level of supplemental damping to the targeted vibration mode and that the attainable damping can be accurately estimated from the two undamped problems associated with vanishing and infinite viscous parameters, respectively.

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Figures

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Fig. 1

(a) Coordinates and degrees-of-freedom and (b) warping displacement of beam

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Fig. 2

Beam with simple supports and reaction stress σd due to warping displacement at x=ℓ

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Fig. 3

Cases (I)–(VI) with a double arrow representing a viscous bimoment

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Fig. 4

Undamped natural frequencies for the first vibration mode

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Fig. 5

Complex frequency loci ((a) and (c)) and damping ratios ((b) and (d)) for kℓ=3 ((a) and (b)) and kℓ=30 ((c) and (d))

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Fig. 6

Frequency loci ((a) and (c)) and damping ratios ((b) and (d)) for kℓ=3 ((a) and (b)) and kℓ=30 ((c) and (d))

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Fig. 7

Maximum damping ratio as function of viscous ratio ν for kℓ=3

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