Optimal designs for non-uniform tuned liquid column dampers in horizontal motion

In this paper, the optimal design parameters of tuned liquid column dampers (TLCD) with non-uniform cross-sections for application to a SDOF structure in horizontal motion are summarized. In the first part, optimization for the interacted structure subjected to harmonic loading is revisited and the computation is facilitated by a non-iterative analytical response solution (closed-form solution) proposed for expediting the process. From both analytical and numerical inspections, some new findings were clearly observed, including (i) the optimal head loss is inversely proportional to excitation amplitude; while the optimal frequency tuning ratio is independent of the excitation level; (ii) the minimal peak amplitude of the structure over all possible frequencies occurs when the two resonant peaks in the structural response are equal, and this applies to both damped and undamped structures; (iii) a uniform TLCD is always the best choice under the same condition of structural damping, mass ratio and horizontal length ratio of the TLCD; and (iv) the optimal performance is the same for the cases with reciprocal cross-section ratios. Based on the conclusion in the first part, the second part presents design tables containing lists of optimal parameters for non-uniform (cross-section ratios 2 and 12) and uniform TLCDs as quick guidelines for practical use. For completeness, these tables were also incorporated with the optimal parameters for TLCDs under a white-noise type of loading, which are excerpted from a previously published research. Some results of parametric studies observed from the design tables were also addressed. Finally, a design example is used to demonstrate the use of these design tables.