The Fluid Behavior of a Non-Orifice TLCD under Harmonic Excitation: From Experiments to Analytical Solution

Tuned liquid column damper (TLCD) is a well-known liquid damper designed to absorb the vibration of structures used in many applications, such as high-story buildings, wind turbines, and offshore platforms, requiring an accurate mathematical determination of the liquid level to model the TLCD structure system motion. The mathematical model of a TLCD is a nonlinear ordinary differential equation, unlike the structure, due to the term containing a viscous damping coefficient, and cannot be solved analytically. In this study, the fluid behavior of a TLCD without an orifice, directly connected to a shaking table under harmonic excitation, was investigated experimentally and a new linearization coefficient was proposed to be used in the mathematical model. First, the nonlinear mathematical model was transformed to a nondimensional form to better analyze the parameter relations, focusing on the steady-state amplitude of the liquid level during the harmonic excitation. The experimental data were then processed using the fourth-order Runge–Kutta method, and a correlation to calculate the viscous damping coefficient was proposed in the dimensionless form. Accordingly, a novel empirical model was proposed for the dimensionless steady-state amplitude of the liquid level using this correlation. Finally, with the help of the proposed correlation and the empirical model, an original linearization coefficient was introduced which does not need experimental data. The nonlinear mathematical model was linearized by using the developed linearization coefficient and solved analytically using the Laplace transform method. The study presents a generalized method for the analytical determination of the liquid level in a non-orifice TLCD under harmonic excitation, using a correlation and an empirical model proposed for the first time in this study, providing a novel and simple solution to be used in the examination of various TLCD structure systems.