Autoparametric resonances in a structure/fluid interaction system carrying a cylindrical liquid tank

The nonlinear-coupled vibrations of an elastic structure and liquid sloshing in a cylindrical container are investigated. The behavior of the liquid surface is governed by a kind of the Mathieu equation because the structure is subjected to a vertical and sinusoidal excitation. Modal equations for liquid sloshing governing the coupled motions are derived when the natural frequency of the structure is equal to twice the natural frequency of an anti-symmetric mode of sloshing. The theoretical resonance curves are determined by using van der Pol's method. The influences of a liquid level and a detuning parameter on the theoretical resonance curves are investigated when only the excitation frequency is selected as a control parameter. The inclination of a frequency response curve depends on the liquid level. Furthermore, a small deviation of the tuning condition may cause amplitude- and phase-modulated motions and chaotic vibrations. This deviation also leads to separate the occurrence region of the coupled vibration into two regions of the excitation frequency. The theoretical resonance curves are quantitatively in agreement with the experimental data. Lastly, the amplitude- and phase-modulated motions and chaotic vibrations were observed in experiments.