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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September 2017
Research-Article
Vibration Control of Two-Degree-of-Freedom Structures Utilizing Sloshing in Nearly Square Tanks
Takashi Ikeda,
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
Hiroshima University,
1-4-1, Kagamiyama, Higashi-Hiroshima,
Hiroshima 739-8527, Japan
e-mail: tikeda@hiroshima-u.ac.jp
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Yuji Harata,
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
Hiroshima University,
1-4-1, Kagamiyama, Higashi-Hiroshima,
Hiroshima 739-8527, Japan
e-mail: harata@hiroshima-u.ac.jp
Search for other works by this author on:
Shota Ninomiya
Shota Ninomiya
Olympus Corporation,
2951, Ishikawa-machi, Hachioji,
Tokyo 192-8507 Japan
2951, Ishikawa-machi, Hachioji,
Tokyo 192-8507 Japan
Search for other works by this author on:
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
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
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
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. Sep 2017, 12(5): 051012 (18 pages)
Published Online: May 4, 2017
Article history
Received:
August 3, 2016
Revised:
March 12, 2017
Citation
Ikeda, T., Harata, Y., and Ninomiya, S. (May 4, 2017). "Vibration Control of Two-Degree-of-Freedom Structures Utilizing Sloshing in Nearly Square Tanks." ASME. J. Comput. Nonlinear Dynam. September 2017; 12(5): 051012. https://doi.org/10.1115/1.4036481
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