Closed-form optimal calibration of a tuned liquid column damper (TLCD) for flexible structures

Abstract The conventional optimal calibration of a TLCD for suppressing structural vibration is based on the classic 2-degrees-of-freedom (2-DOF) model in terms of one specific structural mode (usually the resonant mode). For flexible multi-degrees-of-freedom (MDOF) structures, this implies that background flexibility contribution from other non-resonant modes is omitted, resulting in an unbalance in the frequency response of the flexible structure-TLCD coupled system. Furthermore, numerical search techniques are usually used for optimizing TLCDs, and extensive computational efforts are required. Therefore, in this paper a novel closed-form optimal calibration procedure accounting for the background flexibility contribution from the flexible structure is developed based on the pole-placement method. The background flexibility is represented by an equivalent stiffness that is derived from modal analysis. An analogue 2-DOF model accounting for background flexibility is developed, which turns out to be a generalization of the classic 2-DOF model. The root locus analysis is performed to derive the optimal frequency ratio of the TLCD by the equal modal damping ratio criterion. A straightforward approach for determining the optimal head loss coefficient is proposed based on the bifurcation point present in the root locus. It is seen from the closed-form formulas that the optimal parameters of the TLCD depend not only on the constructive parameters (such as the mass ratio and horizontal length ratio of a TLCD) but also on the structural inherent characteristics. Application to MDOF flexible structures are illustrated by a 10-story shear frame. Results demonstrates that the proposed calibration procedure leads to a balanced frequency response curve and thus improves the performance of the TLCD comparing with the calibration procedure ignoring background flexibility.