Study on Nonlinear Vibrations of Structures Carrying Liquid Tanks

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The nonlinear-coupled vibrations of an elastic structure vertically excited and liquid sloshing in a cylindrical tank are investigated. When the natural frequency of the structure is close to twice the natural frequency of the sloshing, this system exhibits the behavior of an autoparametric system. We treated two cases, i.e., when the axisymmetric mode or the anti-symmetric mode of sloshing mode occurs predominantly., and the resonance curves are presented. The results can be summarized as follows :1.In the theoretical analysis, the modal equations are derived from the partial equations of motion governing the system, taking account of the nonlinearly of liquid force. Then the expressions of the resonance curve are obtained by using the method of harmonic balance and an FFT analysis.2.Harmonic oscillations and 1/2-oder subharmonic oscillations can occur respectively in the structure and the liquid surface, under the tuning condition such that the natural frequencies of the structure and the liquid sloshing have the relation 2 : 1.3.The shape of the resonance curve for the structure changes from a shape with a peak to a flat shape, as the liquid level decreases.4.A certain deviation of the tuning condition may cause amplitude-modulated motions. By introducing the detuning parameter, e.g., σィイD201ィエD2=pィイD20ィエD2-2pィイD201ィエD2 (pィイD20ィエD2 is the natural frequency of the structure, and pィイD201ィエD2 is the natural frequency of the axisymmetric sloshing mode), this kind of motion can appear only for a high liquid level and σィイD201ィエD2<0.5.In the experiments, the theoretical resonance curves were qualitatively in good agreement with the experimental results. In addition, amplitude-modulated motions were observed.