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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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References

Paidoussis, M. P., 1998. Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. 1, Academic, London, UK.
Ibrahim, R. A., Pilipchuk, V. N., and Ikeda, T., 2001, “Recent Advances in Liquid Sloshing Dynamics,” ASME Appl. Mech. Rev., 54(2), pp. 133–199. [CrossRef]
Ibrahim, R. A., 2005, Liquid Sloshing Dynamics, Cambridge University, Cambridge, UK.
Hutton, R. E., 1963, “An Investigation of Resonant, Nonlinear, Nonplanar Free Surface Oscillations of a Fluid,” NASA, Technical Note, D-1870, pp. 1–64.
Abramson, H. N., Chu, W. H., and Kana, D. D., 1966, “Some Studies of Nonlinear Lateral Sloshing in Rigid Containers,” ASME, J. Appl. Mech., 33(4), pp. 777–784. [CrossRef]
Ibrahim, R. A., and Soundararajan, A., 1983, “Non-Linear Parametric Liquid Sloshing Under Wide Band Random Excitation,” J. Sound Vib., 91(1), pp. 119–134. [CrossRef]
Ibrahim, R. A., and Heinrich, R. T., 1988, “Experimental Investigation of Liquid Sloshing Under Parametric Random Excitation,” ASME, J. Appl. Mech., 55, pp. 467–473. [CrossRef]
Sakata, M., Kimura.K., and Utsumi, M., 1984, “Non-Stationary Response of Non-Linear Liquid Motion in a Cylindrical Tank Subjected to Random Base Excitation,” J. Sound Vib., 94(3), pp. 351–363. [CrossRef]
Yamada, Y., Iemura, H., Noda, S., and Shimada, S., 1987, “Long-Period Response Spectra from Nonlinear Sloshing Analysis Under Horizontal and Vertical Excitations,” Nat. Disaster Sci., 9(2), pp. 39–54.
Fujino, Y., Pacheco, M., Sun, Li-Min, Chaiseri, P., and Isobe, M., 1989, “Simulation of Nonlinear Wave in Rectangular Tuned Liquid Damper (TLD) and its Verification,” Trans. Jpn. Soc. Civ. Eng. (in Japanese), 35-A, pp. 561–574.
Hagiuda, H., 1989, “Oscillation Control System Exploiting Fluid Force Generated by Water Sloshing,” Mitsui Zosen Tech. Rev. (in Japanese), 137, pp. 13–20.
Welt, F., and Modi, V. J., 1992, “Vibration Damping Through Liquid Sloshing, Part 1: A Nonlinear Analysis,” ASME J. Vibr. Acoust., 114(1), pp. 10–16. [CrossRef]
Welt, F., and Modi, V. J., 1992, “Vibration Damping Through Liquid Sloshing, Part 2: Experimental Results,” ASME J. Vibr. Acoust., 114(1), pp. 17–23. [CrossRef]
Ikeda, T., and Nakagawa, N., 1997, “Nonlinear Vibrations of a Structure Caused by Water Sloshing in a Rectangular Tank,” J. Sound Vib., 201(1), pp. 23–41. [CrossRef]
Ikeda, T., Hirayama, T., and Nakagawa, N., 1998, “Nonlinear Vibrations of a Structure Caused by Water Sloshing in a Cylindrical Tank,” JSME, Int. J., Series C, 41(3), pp. 639–651. [CrossRef]
Ibrahim, R. A., Gau, J.-S., and Soundararajan, A., 1988, “Parametric and Autoparametric Vibrations of an Elevated Water Tower, Part I: Non-Linear Parametric Resonance,” J. Sound Vib., 121(3), pp. 413–428. [CrossRef]
Ikeda, T., 2003, “Nonlinear Parametric Vibrations of an Elastic Structure With a Rectangular Liquid Tank,” Nonlinear Dyn., 33(1), pp. 43–70. [CrossRef]
Ikeda, T., and Murakami, S., 2005, “Autoparametric Resonances in a Structure/Fluid Interaction System Carrying a Cylindrical Liquid Tank,” J. Sound Vib., 285(3), pp. 517–546. [CrossRef]
Housner, G. W., 1963, “Dynamic Pressure on Fluid Containers,” TID-7027, Nuclear Reactors and Earthquakes, pp. 183–209, US Atomic Energy Comm, Washington, DC.
Kareem, A., and Sun, W. J., 1987, “Stochastic Response of Structures With Fluid-Containing Appendages,” J. Sound Vib., 119(3), 398–408. [CrossRef]
Soundararajan, A., and Ibrahim, R. A., 1988, “Parametric and Autoparametric Vibrations of an Elevated Water Tower, Part III: Random Response,” J. Sound Vib., 121(3), pp. 445–462. [CrossRef]
Ikeda, T., and Ibrahim, R. A., 2005, “Nonlinear Random Responses of a Structure Parametrically Coupled With Liquid Sloshing in a Cylindrical Tank,” J. Sound Vib., 284(1–2), pp. 75–102. [CrossRef]
Koh, C. G., Mahatma, S., and Wang, C. M., 1995, “Reduction of Structural Vibrations by Multiple-Mode Liquid Dampers,” Eng. Struct., 17(2), 122–128. [CrossRef]
Bolotin, V. V., 1964, The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco, CA.
Box, G. E. P., and Müller, M. E., 1958, “A Note on the Generation of Random Normal Deviates,” Ann. Math. Stat., 28, pp. 610–611. [CrossRef]
Faltinsen, O. M., Rognebakke, O. F., Lukovsky, I. A., and Timokha, A. N., 2000, “Multidimensional Modal Analysis of Nonlinear Sloshing in a Rectangular Tank With Finite Water Depth,” J. Fluid Mech., 407, pp. 201–234. [CrossRef]
Ikeda, T., Ibrahim, R. A., Harata, Y., and Kuriyama, T., 2012, “Nonlinear Liquid Sloshing in a Square Tank Subjected to Obliquely Horizontal Excitation,” J. Fluid Mech., 700, pp. 304–328. [CrossRef]
Crandall, S. H. and Mark, W. D., 1963, Random Vibration in Mechanical Systems, Academic, New York.

Figures

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Fig. 1

The model for theoretical analysis

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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. 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. 4

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