Non-linear vibrations of a structure caused by water sloshing in a rectangular tank

The non-linear vibrations of a structure coupled with water sloshing in a rectangular tank are theoretically and experimentally studied. The water tank is attached to a structure to suppress the horizontal vibrations of the structure caused by a sinusoidal excitation. In the theoretical analysis, considering the only source of non-linearity of the liquid inertia to be due to a large sloshing amplitude, the modal equations for sloshing are presented. Secondly, the solutions for the harmonic oscillations of the structure and the water surface are determined, including their stability analyses. Then, the resonance curves for this system are shown. As a result, the resonance curves are found to change from the soft spring type to the hard spring type as the water depth decreases. The resonance curves also show that a super-summed-and-differential harmonic oscillation can occur at the tuning frequency when the magnitude of excitation is comparatively large. This is a kind of non-linear forced oscillation due to the non-linearity of the fluid force. The appearance of this oscillation reduces the efficacy of vibration suppression by using the water tank. In conclusion, it was ascertained that these results agreed qualitatively well with the experimental results. (C) 1997 Academic Press Limited.