Vibration suppression of a 2DOF tower structure subjected to horizontal harmonic excitation utilizing sloshing in a circular cylindrical tank and its limitations

This study investigates the vibration control performance of a partially liquid-filled cylindrical tank, referred to as a tuned liquid damper (TLD), as a device for suppressing vibrations in a two-degree-of-freedom tower-like structure subjected to horizontal harmonic excitation. Under circumstances involving large-amplitude liquid sloshing, the two orthogonal and degenerate (1, 1) sloshing modes undergo nonlinear interactions, thereby exciting the higher-order sloshing modes. Modal equations governing the two principal (1, 1) sloshing modes and three higher-order sloshing modes were derived based on fluid potential theory, together with the equations of motion for the structure in both horizontal directions, considering the effects of fluid nonlinearity. Subsequently, van der Pol’s method is employed to obtain the frequency response curves for the structure’s vibration and liquid sloshing. The findings suggest that when the excitation force is relatively small, the vibration amplitude of the structure near the tuning frequency is significantly reduced. However, at excitation frequencies on either side of the tuning frequency, the structure exhibits bidirectional vibrations induced by the swirl motion of the liquid surface. The manifestation of this phenomenon is dependent on the excitation frequency and amplitude. Additionally, amplitude-modulated motions, including chaotic behavior, may arise at excitation frequencies near the Hopf bifurcation points of the response curves. When an external force of greater magnitude is applied, combination resonance emerges near the tuning frequency, resulting in a decline in the vibration control performance of the TLD. Experiments were subsequently conducted to observe phenomena predicted by theoretical calculations and to validate the theoretical results.