Abstract
Vibration control of an elastic structure subjected to horizontal harmonic excitation by using a nearly square liquid tank is investigated. When the tuning condition, a ratio 1:1:1, is satisfied among the natural frequencies of the structure and two sloshing modes (1,0) and (0,1) in the tank, the performance of the tuned liquid damper can be improved because autoparametric resonance occurs. In the theoretical analysis, the equation of motion for the structure and the modal equations for sloshing are derived considering the nonlinearity of sloshing. Then, van der Pol's method is employed to determine the frequency response curves. The influences of the system parameters, such as the aspect ratio of the tank cross-section and the installation angle of the tank, on the response curves are examined. As a result, the optimal values of these parameters are determined. Hopf bifurcations occur and amplitude modulated motions appear depending on the system parameters. The validity of the theoretical results was confirmed by the experimental data.
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