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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August 2017
Research-Article
Vibration Control of Horizontally Excited Structures Utilizing Internal Resonance of Liquid 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:
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
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. Aug 2017, 139(4): 041009 (13 pages)
Published Online: May 30, 2017
Article history
Received:
September 14, 2016
Revised:
February 15, 2017
Citation
Ikeda, T., and Harata, Y. (May 30, 2017). "Vibration Control of Horizontally Excited Structures Utilizing Internal Resonance of Liquid Sloshing in Nearly Square Tanks." ASME. J. Vib. Acoust. August 2017; 139(4): 041009. https://doi.org/10.1115/1.4036211
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