Nonlinear parametric vibrations of an elastic structure with a rectangular liquid tank

The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a rectangular tank partially filled with liquid, are investigated. The structure on which the liquid tank is attached is vertically subjected to a sinusoidal excitation when the natural frequency of the structure is equal to twice the natural frequency of one of the sloshing modes. In the theoretical analysis, the modal equations are derived by taking nonlinear fluid force into account. Responses of the structure and the liquid surface are presented as resonance curves using the harmonic balance method. From this theoretical analysis the following predictions are obtained: (a) due to the nonlinearity of the fluid force, harmonic oscillations appear in the structure, while subharmonic oscillations occur on the liquid surface; (b) the shapes of the resonance curves markedly change depending on the liquid level; and (c) when the tuning condition is slightly deviated, amplitude modulated motions and chaotic oscillations appear during a certain range of the excitation frequency. These were qualitatively in agreement with the experimental results.