Development and validation of a nonlinear dynamic model for tuned liquid multiple columns dampers

The tuned liquid column damper (TLCD), a passive damping device consisting of a large U-tube with oscillating liquid, has been shown to be effective at mitigating structural responses under natural hazards. Aside from their bandwidth-limited mitigation capabilities, a key limitation of TLCDs is in their large geometries that occupy large space often at prime locations. A solution is to implement multi-columned versions, termed tuned liquid multiple columns dampers (TLMCDs), which have the potential to be tuned to multiple frequencies and occupy less space by leveraging the multiple columns to allow fluid movement. However, mathematical models characterizing their dynamic behavior must be developed enabling proper tuning and sizing in the design process. In this paper, a new analytical model characterizing a TLMCD as a multiple degrees-of-freedom coupled nonlinear system is presented. The frequencies of free vibration and vibration modes of a TLMCD are identified in closed-form formulations. Results are validated using computational fluid dynamics simulations, and show that the analytical model can predict the damper’s liquid surface movements as well as its capability to reduce structural vibration when the structure is subjected to harmonic excitations. A parametric study is conducted to investigate the effect of head loss coefficients, column spacing, cross-section area ratios, and column numbers on mitigating structural response. It is found that, while TLMCDs are less effective than traditional TLCDs under an equal liquid mass, they can provide enhanced performance under geometric restrictions