Theoretical and experimental investigation of flexible air spring stiffness in a tuned liquid column gas damper for vertical vibration control

This study investigates the effectiveness of equivalent linear air spring stiffness in a Vertical Tuned Liquid Column Gas Damper (VTLCGD) for reducing vertical structural vibrations, particularly considering different sealing conditions. The VTLCGD system, designed with a single sealed vertical air column, allows flexible frequency tuning by adjusting the air spring stiffness. It aims to be used in low-frequency structures where conventional VTLCGD designs with two sealed ends are less efficient. The geometric configuration and working principle of the VTLCGD are first described. The equation of motion is derived using liquid dynamic equilibrium and the pressure-volume relationship, with expressions for natural frequency and control force validated through shaking table tests conducted with varying VTLCGD lengths. Experimental investigations are conducted to examine the parameters affecting damper performance using pressure data. The system's vibration reduction performance is then numerically evaluated on a cantilevered floor subjected to human walking. The numerical results, based on the equation of motion for liquid displacement and natural frequency, show good agreement with experimental data, which confirms the effectiveness of using linearized air spring stiffness for frequency tuning. The effects of total liquid length and height difference on control force are further investigated, and a polytropic index of 1.2 is determined for the VTLCGD frequency formula. The VTLCGD system achieves a maximum vibration reduction of 52.63 % in acceleration response on the cantilevered floor compared to the uncontrolled case. Moreover, the variation in stiffness due to changes in the sealing condition is presented to validate the damper's adaptability over a wide frequency range.