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Research Papers: Flows in Complex Systems

Mitigation of Vortex-Induced Vibrations of a Pivoted Circular Cylinder Using an Adaptive Pendulum Tuned-Mass Damper

[+] Author and Article Information
Sina Kheirkhah

e-mail: skheirkh@uwaterloo.ca

Richard Lourenco

e-mail: rlourenco@uwaterloo.ca

Serhiy Yarusevych

e-mail: syarus@uwaterloo.ca
Department of Mechanical
and Mechatronics Engineering,
University of Waterloo,
200 University Avenue West,
Waterloo, Ontario N2L 3G1, Canada

Sriram Narasimhan

Department of Civil and
Environmental Engineering,
University of Waterloo,
200 University Avenue West,
Waterloo, Ontario N2L 3G1, Canada
e-mail: snarasim@uwaterloo.ca

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 27, 2012; final manuscript received July 17, 2013; published online September 6, 2013. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 135(11), 111106 (Sep 06, 2013) (15 pages) Paper No: FE-12-1157; doi: 10.1115/1.4025059 History: Received March 27, 2012; Revised July 17, 2013

A novel adaptive pendulum tuned-mass damper (TMD) was integrated with a two degree-of-freedom (DOF) cylindrical structure in order to control vortex-induced vibrations of the structure. The natural frequency of the TMD was adjusted autonomously in order to control the vortex-induced vibrations. The experiments were performed at a constant Reynolds number of 2100 and for four reduced velocities, 4.18, 5.44, 6.00, and 6.48. Two TMD damping ratios, 0 and 0.24, were investigated for a constant TMD mass ratio of 0.087. The results demonstrate that tuning the natural frequency of the TMD to the natural frequency of the structure decreases the amplitudes of transverse and streamwise vibrations of the structure significantly. Specifically, the transverse amplitudes of vibrations are decreased by a factor of ten and streamwise amplitudes of vibrations are decreased by a factor of three. Depending on the value of the TMD damping ratio, the frequency of transverse vibrations is either characterized by the natural frequency of the structure or by two other fundamental frequencies, one higher and the other lower than the natural frequency of the structure. The results demonstrate that, independent of the TMD damping and tuning frequency ratios, the frequency of streamwise vibrations matches that of the transverse vibrations in the synchronization region, and the cylinder traces elliptic trajectories. A mathematical model is proposed to gain insight into the frequency response of the structure and fluid-structure interactions. The model shows that, for low TMD damping ratios, the frequency response of the structure equipped with the TMD is characterized by two fundamental frequencies; whereas, for relatively high TMD damping ratios, the frequency response of the structure is characterized by a single frequency, i.e., the natural frequency. In both cases, the fluid forcing within the synchronization region is linked to the fundamental frequency/frequencies of the structure. Thus, the classical definition of synchronization applies to multiple DOF structures undergoing vortex-induced vibrations.

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Figures

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Fig. 1

Schematics of (a) tunes-mass damper and (b) pendulum tuned-mass damper

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Fig. 2

Experimental arrangement: (a) cylinder model mounted in the water flume test section without a PTMD and (b) simplified top view schematics

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Fig. 3

Adaptive pendulum tuned-mass damper attached to the top of the cylinder model

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Fig. 4

(a) Transverse and (b) streamwise amplitudes of vibrations for 1/fr* = 0 (restrained pendulum) and 1/fr* = 1 (pendulum natural frequency tuned to the natural frequency of the structure). The structure damping ratio (ζ) varies between 0.004 and 0.018.

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Fig. 5

Normalized amplitudes of vibrations. (•) corresponds to increasing 1/fr* and (□) corresponds to decreasing 1/fr*.

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Fig. 6

Normalized transverse vibrations for (a) ζTMD = 0.24 and (b) ζTMD = 0

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Fig. 7

Normalized frequency of transverse vibrations at U* = 6.00 for (a) ζTMD = 0.24 and (b) ζTMD = 0. (•) corresponds to increasing 1/fr* and (□) corresponds to decreasing 1/fr*

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Fig. 8

Spectrogram of transverse vibrations at U* = 6.00, ζTMD = 0.24, and 1/fr*=1

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Fig. 9

Spectrograms and spectra of transverse vibrations for increasing values of 1/fr* at U* = 6.00 and ζTMD = 0. The spectrograms pertain to 1/fr* values indicated in the corresponding spectral plots.

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Fig. 10

Spectrograms and spectra of transverse vibrations for decreasing values of 1/fr*, at U* = 6.00 and ζTMD = 0. The spectrograms pertain to 1/fr* values indicated in the corresponding spectral plots.

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Fig. 11

Spectra of streamwise and transverse vibrations at U* = 6.00 and 1/fr* = 1.1 for (a) ζTMD = 0.24 and (b) ζTMD = 0

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Fig. 12

Cylinder tip trajectories for ζTMD = 0.24

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Fig. 13

Cylinder tip trajectories for U* = 6.00 and ζTMD = 0

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Fig. 14

Phase angles for ζTMD = 0.24

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Fig. 15

Phase angles for U* = 6.00 and ζTMD = 0

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Fig. 16

Schematics of the cylindrical structure equipped with the tuned-mass damper

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Fig. 17

Model predictions for frequency of transverse free vibrations of the structure at 1/fr* = 1.1

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Fig. 18

Model predictions for frequency of transverse free vibrations of the structure for (a) ζTMD = 0.24 and (b) ζTMD = 0

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Fig. 19

Frequency of transverse and streamwise forced vibrations of the structure at 1/fr* = 0.52, fe,x* = 0.4, and fe,y* = 2.3 for (a,c) ζTMD = 0.24 and (b,d) ζTMD = 0

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Fig. 20

Model predictions for spectra of (a) transverse vibrations and (b) streamwise vibrations at ζTMD = 0.24

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Fig. 21

Model predictions for spectra of (a) transverse and (b) streamwise vibrations for ζTMD = 0 and 1/fr* = 1.1

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