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Research Papers: Seismic Engineering

Passive Vibration Control of Structures Subjected to Random Ground Excitation Utilizing Sloshing in Rectangular Tanks

[+] Author and Article Information
Takashi Ikeda

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

Raouf A. Ibrahim

Department of Mechanical Engineering,
Wayne State University,
Detroit, MI 48202

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 4, 2012; final manuscript received July 12, 2013; published online October 23, 2013. Assoc. Editor: Chong-Shien Tsai.

J. Pressure Vessel Technol 136(1), 011801 (Oct 23, 2013) (11 pages) Paper No: PVT-12-1089; doi: 10.1115/1.4025083 History: Received July 04, 2012; Revised July 12, 2013

Passive vibration control of an elastic structure carrying a rectangular tank, partially filled with liquid, is investigated when the structure is subjected to horizontal, narrowband, random ground excitation. The modal equations of motion for liquid sloshing are derived using Galerkin's method, considering the nonlinearity of sloshing. The system response statistics including mean square values, correlation coefficients, and probability density functions (PDFs) are numerically estimated from the time histories using the Monte Carlo simulation when the natural frequency of the structure is close to that of liquid sloshing. The influences of the excitation center frequency, its bandwidth, and the liquid level on the system responses are examined. As a result, it is found that the mean square responses of the structure decrease when the center frequency is close to the natural frequency of the structure due to sloshing. Tuned liquid dampers (TLDs) are found to be most effective for comparatively low liquid levels.

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Figures

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Fig. 1

The model for theoretical analysis

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Fig. 7

Mean square response for the structure displacement and mean square responses and for the liquid elevation, same as in Fig. , but γ = 0.08

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Fig. 8

Mean square response for the structure displacement and mean square responses and for the liquid elevation, same as in Fig. , but γ = 0.10

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Fig. 9

Ratio of in a coupled system to in an uncoupled system for various values of bandwidth γ = 0.06, 0.05, and 0.10 in Figs. 3, 7, and 8, respectively

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Fig. 10

Probability density distributions of the structure displacement xs and the liquid elevation η showing the influence of the center frequency Ω in Fig. : (a) Ω = 0.925, (b) Ω = 1.000, and (c) Ω = 1.075

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Fig. 11

Probability density distributions of the amplitudes of xs and b1 for different values of the center frequency Ω in Fig. : (a) Ω = 0.925, (b) Ω = 1.000, and (c) Ω = 1.075

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Fig. 12

Mean square response E[xs2] for the structure displacement and mean square responses E[b12] and E[η2] for the liquid elevation, same as in Fig. 3 , but (a) h = 0.33 and w = 0.182; (b) h = 0.2 and w = 0.3

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Fig. 3

Mean square response for the structure displacement and mean square responses for the liquid elevation at x = 0.5 and for the first sloshing mode, showing the influence of the center frequency Ω, when γ = 0.06. The values of the other parameters are the same as those in Fig. 2.

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Fig. 2

A comparison of the mean square response E[xs2] for the uncoupled system and the numerical simulation result when μ = 0.94, ks = 1.0, cs = 0.013, L = 20, h = 0.6, w = 0.1, ζi = 0.015, γ = 0.06, and S0 = 1.0 × 108

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Fig. 6

Correlation coefficients ρ(-x··g,xs) , ρ(-x··g,b1), and ρ(xs,b1), same as in Fig. 3

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Fig. 5

Enlarged time histories of Fig. at (a) Ω = 0.925 and (b) Ω = 1.075

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Fig. 4

Time histories at (a) Ω = 0.925, (b) Ω = 1.000, and (c) Ω = 1.075 in Fig. 3

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