Analytical Solution of the Closed-Form Equations Governing the Hybrid Performance of a Tuned Liquid Column Gas Damper Equipped With a Variable Orifice

Abstract

Structural vibrations are one of the main concerns of engineering in recent decades. The tendency towards a flexible structure such as tall structures or structures with long spans has caused in more intense movements of the structure under service loading. Limiting acceleration in tall and slender buildings, as well as controlling vibrations, is a complex design issue. In this research, the new hybrid damper; "tuned liquid column gas damper equipped with variable orifice (H-O-TLCGD)" is introduced. The dominant mechanism for confronting with vibration in this damper is based on liquid movement, and the vibration energy is dissipated by the effects of fluid turbulence and friction caused by the local pressure drop of the orifice opening. In order to achieve the actual performance behavior of the system, the equations governing the dynamic response of the structure equipped with this damper are obtained along with damping modification and removation of some uncertainties, which cause non-linear equations. Also, in this research, according to the advantages of low energy demand, permanent stability of the system and economic efficiency of using semi-active control systems, the combination of semi-active and passive dampers and the increase of stiffness in the systems equipped with them by gas springs, with the aim of improving the performance of system are considered so that the performance level of structures equipped with this new control system improve at an acceptable level. This research presents the differential equations governing the axial performance of the liquid column damper, accounting for energy dissipation due to changes in flow cross-section and gas spring stiffness, and demonstrates how to combine these effects using hydrodynamics and structural control principles. Also, the closed-form analytical solution of these nonlinear equations is presented so that researchers can achieve their research goals in a shorter time. To facilitate practical applications, this research provides a methodology for designing systems equipped with this damper and optimizing its performance using semi-active control effects, which will be useful for researchers and construction engineers.