Non-linear dynamic responses of elastic two-story structures with partially filled liquid tanks

This paper deals with the non-linear vibrations of an elastic two-story structure with two liquid tanks installed under horizontal harmonic excitation. The influence of the configuration of the two rectangular tanks on the response of the structure is investigated. In the theoretical analysis, Galerkin's method is applied to derive the equations of motion for the structure and the modal equations for sloshing, while considering the non-linear liquid forces. Then, van der Pol's method is used to determine the frequency response curves. Three cases are investigated: In the first case two tanks are installed, one on the top and one on the second story of the structure, in the second case one tank is installed on top, and in the third case two tanks are installed on top. The theoretical results of the first case are compared with those of the second and third cases. In the numerical calculations, it is found that Hopf bifurcations occur near the tuning frequency and then amplitude modulated motion appears in both the first and third cases. It is thus concluded that multiple tanks yield less effectiveness in suppressing the vibrations of the structure. The experimental data confirm the validity of the theoretical results for the first and third cases.