Campus Units

Civil, Construction and Environmental Engineering, Electrical and Computer Engineering, Center for Nondestructive Evaluation (CNDE)

Document Type


Publication Version

Submitted Manuscript

Publication Date


Journal or Book Title

Journal of Sound and Vibration



First Page





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.

Research Focus Area

Structural Engineering


This is a manuscript of an article published as Cao, Liang, Yongqiang Gong, Filippo Ubertini, Hao Wu, An Chen, and Simon Laflamme. "Development and validation of a nonlinear dynamic model for tuned liquid multiple columns dampers." Journal of Sound and Vibration 487 (2020): 115624. DOI: 10.1016/j.jsv.2020.115624. Posted with permission.

Copyright Owner

Elsevier Ltd.



File Format


Published Version