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Research Papers

Vibration Control of Horizontally Excited Structures Utilizing Internal Resonance of Liquid Sloshing in Nearly Square Tanks

[+] Author and Article Information
Takashi Ikeda

Department of Mechanical Systems Engineering,
Hiroshima University,
1-4-1, Kagamiyama,
Higashi-Hiroshima, Hiroshima 739-8527 Japan
e-mail: tikeda@hiroshima-u.ac.jp

Yuji Harata

Department of Mechanical Systems Engineering,
Hiroshima University,
1-4-1, Kagamiyama,
Higashi-Hiroshima, Hiroshima 739-8527 Japan
e-mail: harata@hiroshima-u.ac.jp

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 14, 2016; final manuscript received February 15, 2017; published online May 30, 2017. Assoc. Editor: Miao Yu.

J. Vib. Acoust 139(4), 041009 (May 30, 2017) (13 pages) Paper No: VIB-16-1457; doi: 10.1115/1.4036211 History: Received September 14, 2016; Revised February 15, 2017

Passive control of vibrations in an elastic structure subjected to horizontal, harmonic excitation by utilizing a nearly square liquid tank is investigated. When the natural frequency ratio 1:1:1 is satisfied among the natural frequencies of the structure and the two predominant sloshing modes (1,0) and (0,1), the performance of a nearly square tank as a tuned liquid damper (TLD) is expected to be superior to rectangular TLDs due to internal resonance. In the theoretical analysis, Galerkin's method is used to determine the modal equations of motion for liquid sloshing considering the nonlinearity of sloshing. Then, van der Pol's method is used to obtain the expressions for the frequency response curves for the structure and sloshing modes. Frequency response curves and bifurcation set diagrams are shown to investigate the influences of the aspect ratio of the tank cross section and the tank installation angle on the system response. From the theoretical results, the optimal values of the system parameters can be determined in order to achieve maximum efficiency of vibration suppression for the structure. Hopf bifurcations occur and amplitude modulated motions (AMMs) may appear depending on the values of the system parameters. Experiments were also conducted, and the theoretical results agreed well with the experimental data.

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Figures

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Fig. 2

Mode shapes of sloshing: (a) (1,0) mode and (b) (0,1) mode

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Fig. 3

Frequency response curves for (a) amplitude A0 of the structure, (b) amplitude A10 of (1,0) mode, and (c) amplitude A01 of (0,1) mode when μ0 = 0.94, μ1 = 0.06, k = 1.0, c = 0.013, h = 0.6, w = 2.0, ζij = 0.014, F0 = 0.0015, and α = 0 deg

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Fig. 4

Frequency response curves when only the value of the tank breadth w = 2.0 in Fig. 3 is changed to w = 1.0

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Fig. 5

Stationary time histories at ω = 1.070 on stable branch HiCi in Figs. 3 and 4: (a) time histories in Fig. 3 and (b) time histories in Fig. 4

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Fig. 6

Frequency response curves when only the value of the tank breadth w = 1.0 in Fig. 4 is changed to w = 0.87

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Fig. 7

Frequency response curves when only the value of the tank breadth w = 1.0 in Fig. 4 is changed to w = 0.80

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Fig. 8

Stationary time histories on unstable branch DiHi in Fig.7: (a) ω = 1.060 and (b) ω = 1.075

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Fig. 9

Bifurcation sets in the (ω, w) plane for α = 0 deg near the right peak

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Fig. 10

Frequency response curves when only the value of the tank installation angle α = 0 deg in Fig. 6 is changed to α = 10 deg

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Fig. 11

Frequency response curves when only the value of the tank installation angle α = 0 deg in Fig. 6 is changed to α = 30 deg

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Fig. 12

Bifurcation sets in the (ω, α) plane for w = 0.87

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Fig. 13

Frequency response curves when only the value of the tank breadth w = 1.0 in Fig. 4 is changed to w = 1.13

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Fig. 14

Frequency response curves when only the value of the tank installation angle α = 0 deg in Fig. 13 is changed to α = 60 deg

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Fig. 15

Experimental apparatus: (a) schematic diagram and (b) photo

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Fig. 16

Frequency response curves for apparatus A

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Fig. 17

Frequency response curves for apparatus B

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Fig. 18

Frequency response curves for apparatus C

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