Nonlinear vibrations of an elastic structure with two partially filled liquid tanks subjected to horizontal harmonic excitation are investigated. The natural frequencies of the structure and sloshing satisfy the tuning condition 1:1:1 when tuned liquid dampers are used. The equations of motion for the structure and the modal equations of motion for the first, second, and third sloshing modes are derived by using Galerkin’s method, taking into account the nonlinearity of the sloshing. Then, van der Pol’s method is employed to determine the frequency response curves. It is found in calculating the frequency response curves that pitchfork bifurcation can occur followed by “localization phenomenon” for a specific excitation frequency range. During this range, sloshing occurs at different amplitudes in the two tanks, even if the dimensions of both tanks are identical. Furthermore, Hopf bifurcation may occur followed by amplitude- and phase-modulated motions including chaotic vibrations. In addition, Lyapunov exponents are calculated to prove the occurrence of both amplitude-modulated motions and chaotic vibrations. Bifurcation sets are also calculated to show the influence of the system parameters on the frequency response. Experiments were conducted to confirm the validity of the theoretical results. It was found that the theoretical results were in good agreement with the experimental data.
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April 2011
Research Papers
Nonlinear Dynamic Responses of Elastic Structures With Two Rectangular Liquid Tanks Subjected to Horizontal Excitation
Takashi Ikeda
Takashi Ikeda
Mechanical Systems Engineering, Faculty of Engineering,
e-mail: tikeda@hiroshima-u.ac.jp
Hiroshima University
, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan
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Takashi Ikeda
Mechanical Systems Engineering, Faculty of Engineering,
Hiroshima University
, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japane-mail: tikeda@hiroshima-u.ac.jp
J. Comput. Nonlinear Dynam. Apr 2011, 6(2): 021001 (15 pages)
Published Online: October 15, 2010
Article history
Received:
July 22, 2009
Revised:
May 28, 2010
Online:
October 15, 2010
Published:
October 15, 2010
Citation
Ikeda, T. (October 15, 2010). "Nonlinear Dynamic Responses of Elastic Structures With Two Rectangular Liquid Tanks Subjected to Horizontal Excitation." ASME. J. Comput. Nonlinear Dynam. April 2011; 6(2): 021001. https://doi.org/10.1115/1.4002382
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