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Research Papers

Vibration Control of Two-Degree-of-Freedom Structures Utilizing 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

Shota Ninomiya

Olympus Corporation,
2951, Ishikawa-machi, Hachioji,
Tokyo 192-8507 Japan

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 3, 2016; final manuscript received March 12, 2017; published online May 4, 2017. Assoc. Editor: Mohammad Younis.

J. Comput. Nonlinear Dynam 12(5), 051012 (May 04, 2017) (18 pages) Paper No: CND-16-1367; doi: 10.1115/1.4036481 History: Received August 03, 2016; Revised March 12, 2017

This paper investigates the vibration control of a towerlike structure with degrees of freedom utilizing a square or nearly square tuned liquid damper (TLD) when the structure is subjected to horizontal, harmonic excitation. In the theoretical analysis, when the two natural frequencies of the two-degree-of-freedom (2DOF) structure nearly equal those of the two predominant sloshing modes, the tuning condition, 1:1:1:1, is nearly satisfied. Galerkin's method is used to derive the modal equations of motion for sloshing. The nonlinearity of the hydrodynamic force due to sloshing is considered in the equations of motion for the 2DOF structure. Linear viscous damping terms are incorporated into the modal equations to consider the damping effect of sloshing. Van der Pol's method is employed to determine the expressions for the frequency response curves. The influences of the excitation frequency, the tank installation angle, and the aspect ratio of the tank cross section on the response curves are examined. The theoretical results show that whirling motions and amplitude-modulated motions (AMMs), including chaotic motions, may occur in the structure because swirl motions and Hopf bifurcations, followed by AMMs, appear in the tank. It is also found that a square TLD works more effectively than a conventional rectangular TLD, and its performance is further improved when the tank width is slightly increased and the installation angle is equal to zero. Experiments were conducted in order to confirm the validity of the theoretical results.

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References

Modi, V. J. , and Welt, F. , 1987, “ Vibration Control Using Nutation Dampers,” International Conference on Flow Induced Vibration, Cumbria, England, May 12–14, pp. 369–376.
Hagiuda, H. , 1989, “ Oscillation Control System Exploiting Fluid Force Generated by Water Sloshing,” Mitsui Zosen Tech. Rev., 137, pp. 13–20 (in Japanese).
Ibrahim, R. A. , 2005, Liquid Sloshing Dynamics, Cambridge University Press, Cambridge, UK.
Sun, L. M. , Fujino, Y. , Pachenco, B. M. , and Isobe, M. , 1989, “ Nonlinear Waves and Dynamic Pressures in Rectangular Tuned Liquid Damper (TLD)—Simulation and Experimental Verification,” Struct. Eng./Earthquake Eng., 6(2), pp. 251s–262s.
Chaiseri, P. , Fujino, Y. , Pachenco, B. M. , and Sun, L. M. , 1989, “ Interaction of Tuned Liquid Damper (TLD) and Structure—Theory, Experimental Verification and Application,” Struct. Eng./Earthquake Eng., 6(2), pp. 273s–282s.
Jin-Kyu, Y. , 1997, “ Nonlinear Characteristics of Tuned Liquid Dampers,” Ph.D. thesis, University of Washington, Department of Civil Engineering, Seattle, WA.
Reed, D. , Yu, J. , Yeh, H. , and Gardarsson, S. , 1998, “ Investigation of Tuned Liquid Dampers Under Large Amplitude Excitation,” J. Eng. Mech., 124(4), pp. 405–413. [CrossRef]
Jin-Kyu, Y. , Wakahara, T. , and Reed, D. A. , 1999, “ A Non-Linear Numerical Model of the Tuned Liquid Damper,” Trans. ASCE J. Struct. Eng., 28(6), pp. 671–686.
Stoker, J. J. , 1950, Nonlinear Vibrations, Wiley, New York.
Ikeda, T. , and Nakagawa, N. , 1997, “ Non-Linear Vibrations of a Structure Caused by Water Sloshing in a Rectangular Tank,” J. Sound Vib., 201(1), pp. 23–41. [CrossRef]
Kaneko, S. , and Yoshida, O. , 1999, “ Modeling of Deepwater-Type Rectangular Tuned Liquid Damper With Submerged Nets,” ASME J. Pressure Vessel Technol., 121(4), pp. 413–422. [CrossRef]
Frandsen, J. B. , 2005, “ Numerical Predictions of Tuned Liquid Tank Structural Systems,” J. Fluids Struct., 20(3), pp. 309–329. [CrossRef]
Fujino, Y. , and Sun, L. M. , 1993, “ Vibration Control by Multiple Tuned Liquid Dampers (MTLDs),” Trans. ASCE J. Struct. Eng., 119(12), pp. 3482–3502. [CrossRef]
Ikeda, T. , 2011, “ Nonlinear Dynamic Responses of Elastic Structures With Two Rectangular Liquid Tanks Subjected to Horizontal Excitation,” ASME J. Comput. Nonlinear Dyn., 6(2), p. 021001. [CrossRef]
Koh, C. G. , Mahatma, S. , and Wang, C. M. , 1995, “ Reduction of Structural Vibrations by Multiple-Mode Liquid Dampers,” Eng. Struct., 17(2), pp. 122–128. [CrossRef]
Ikeda, T. , 2010, “ Non-Linear Dynamic Responses of Elastic Two-Story Structures With Partially Filled Liquid Tanks,” Int. J. Non-Linear Mech., 45(3), pp. 263–278. [CrossRef]
Faltinsen, O. M. , Rognebakke, O. F. , and Timokha, A. N. , 2003, “ Resonant Three-Dimensional Nonlinear Sloshing in a Square-Base Basin,” J. Fluid Mech., 487, pp. 1–42. [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]
Tait, M. J. , El Damatty, A. A. , and Isyumov, N. , 2005, “ An Investigation of Tuned Liquid Dampers Equipped With Damping Screens Under 2D Excitation,” Earthquake Eng. Struct. Dyn., 34(7), pp. 719–735. [CrossRef]
Ikeda, T. , 2010, “ Vibration Suppression of Flexible Structures Utilizing Internal Resonance of Liquid Sloshing in a Nearly Square Tank,” ASME Paper No. PVP2010-25616.
Hutton, R. E. , 1963, “ An Investigation of Resonant, Nonlinear, Nonplanar Free Surface Oscillations of a Fluid,” Space Technology Labs., Inc., Redondo Beach, CA, NASA Technical Report No. NASA-TN-D-1870.
Tondl, A. , Ruijgrok, T., Verhulst, F., and Nabergoj, R., 2000, Autoparametric Resonance in Mechanical Systems, Cambridge University Press, Cambridge, UK.
Faltinsen, O. M. , Rognebakke, O. F. , and Timokha, A. N. , 2006, “ Transient and Steady-State Amplitudes of Resonant Three-Dimensional Sloshing in a Square Base Tank With a Finite Fluid Depth,” Phys. Fluids, 18(1), p. 012103. [CrossRef]
Brent, R. P. , 1973, Algorithms for Minimization Without Derivatives, Prentice-Hall, Englewood Cliffs, NJ, Chap. 4.
Doedel, E. J. , Champneys, A. R. , Fairgrieve, T. F. , Kuznetsov, Y. A. , Sandstede, B. , and Wang, X. , 1997, “ AUTO97: Continuation and Bifurcation Software for Ordinary Differential Equations (With HomCont),” Concordia University, Montreal, QC, Canada.
Faltinsen, O. M. , and Timokha, A. N. , 2009, Sloshing, Cambridge University Press, Cambridge, UK.

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 amplitudes in: (a) structure xs, (b) structure ys, (c) (1,0) mode, and (d) (0,1) mode when μ0 = 0.94, μ1 = 0.06, kx = ky = 1.0, cx = cy = 0.013, w = 0.6, h = 0.6, ζij = 0.015, a0 = 0.0015, and α = 0 deg

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Fig. 4

Same as Fig. 3, but w = 1.0

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Fig. 5

Phase angle curves corresponding to Fig. 4

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Fig. 6

Stationary time histories including ηx at (x, y) = (1/2, 0) and ηy at (x, y) = (0, w/2) and orbits in the (xs, ys) and (ηx, ηy) planes in Figs. 4 and 5: (a) CW rotation at ω = 1.090 on branches HiDi, (b) CCW rotation at ω = 1.090 on branches H′jG′j, (c) regular AMMs swirl at ω = 1.070 on branches GiHi, (d) chaotic AMMs ω = 1.067 on branches GiHi, and (e) CCW rotation at ω = 0.935 on branches EiBi

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Fig. 7

Frequency response curves for amplitudes As and Amax and the orbits of the structure in the (xs, ys) plane: (a) frequency response curves for amplitudes As and Amax, (b) the orbit at ω = 1.090, and (c) the orbit at ω = 0.935

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Fig. 8

Same as Fig. 4, but α = 15 deg

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Fig. 9

Same as Fig. 4, but α = 45 deg

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Fig. 10

Bifurcation sets in the (ω, α) plane

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Fig. 11

Coordinate system in the case of bidirectional excitation

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Fig. 12

Same as Fig. 4, but w = 1.08

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Fig. 13

Same as Fig. 4, but w = 0.935

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Fig. 14

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

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Fig. 15

Experiment setup: (a) schematic diagram and (b) photo

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Fig. 16

Frequency resonance curves for apparatus A

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Fig. 17

Frequency resonance curves for apparatus B

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Fig. 18

Stationary time histories and Lissajous curves in the (xs, ys) and (ηx, ηy) planes observed in Fig. 16: (a) ω = 2.971 Hz and (b) ω = 2.921 Hz

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Fig. 19

Frequency resonance curves for apparatus C

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Fig. 20

Frequency resonance curves for apparatus D

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