Frequency domain non-linear modelling and analysis of liquid filled column dampers

Tuned liquid column dampers (TLCDs) have an extensive usage as an effective vibration absorber to enhance the structure response under the effect of seismic or wind loads. In this study, parameter optimization of nonlinear model of a TLCD in frequency domain under harmonic excitation is proposed in order to improve performance of TLCDs. The non-linearity in the model is due to the head-loss caused by the orifice resulting in velocity squared damping. A 6-story building with a TLCD is considered as a case study. Describing Function Method (DFM) is used to model the nonlinear effects in frequency domain which results in a set of nonlinear algebraic equations. The resulting set of nonlinear equations is solved by Newton’s method utilizing Homotopy Continuation. The effect of change of TLCD parameters (cross-sectional area, head loss coefficient, total length, horizontal length) on the overall system response is investigated through the developed non-linear model. TLCD parameters are optimized utilizing genetic algorithm and gradient descent optimization methods. Response of the optimized and non-optimized models is compared in frequency domain. The linear and non-linear models are also compared and the necessity of introducing non-linearity to the frequency domain model is addressed