Tuned Liquid Column Dampers under Stochastic Excitation with Viscosity and Geometric Effects

Abstract

Tuned Liquid Column Dampers (TLCDs) are recognized for their effectiveness in passive vibration control. However, accurately modeling their damping characteristics remains a challenge due to the complex, nonlinear dependence of head loss on fluid properties and flow regimes. This study presents a numerical framework to evaluate the dynamic response of a primary structure coupled with a TLCD under stochastic excitation, to assess the TLCD's effectiveness in passive vibration control. Unlike traditional approaches that assume a constant experimental damping coefficient, this work employs a phenomenological model that dynamically evaluates the instantaneous head loss using fundamental fluid mechanics principles, employing the Poiseuille and Swamee-Jain formulations for laminar and turbulent regimes, respectively. The resulting system of stiff, nonlinear differential equations is solved using the Backward Differentiation Formula (BDF) method. A comparative analysis of four working fluids (water, ethylene glycol, SAE 30 oil, and glycerin) was conducted to investigate the impact of viscosity on efficiency. For the chosen standard configuration, with a small-diameter tube setup ($D \approx 21$ mm), the results indicate that simply substituting water with high-viscosity fluids increases the simulated structural response. Furthermore, a refined parametric search varying the liquid column length ($L$) and tube diameter ($D$) generated performance heatmaps for Root Mean Square (RMS) and Maximum Absolute (MaxAbs) displacement metrics. These maps showed that lower-response TLCD configurations depend on both the fluid properties and the selected metric. The proposed methodology provides a tool for preliminary TLCD design studies based on explicit assumptions in fluid mechanics.