Optimal design and performance of liquid column mass dampers for rotational vibration control of structures under white noise excitation

The effectiveness under optimal design of a Tuned Liquid Column Damper (TLCD) and a Liquid Column Vibration Absorber (LCVA), in suppressing structural rotational vibrations under white noise excitation are studied in this paper. The effects of deviating from the optimal design under white noise and the effect of the excitation intensity are also addressed. The analytical model is first developed for a structure with a damper. The nonlinear governing equation of the relative motion of the liquid column is linearized and the problem is analyzed in the frequency domain. A method to find optimal values for the tuning ratio, f, and the head loss coefficient, ζ, is developed and studied, considering the complications that are induced by the initial nonlinear form of the governing equations. The controlled performance of the LCVA and TLCD, with optimum values of f and ζ, are numerically investigated through an extensive parametric study. Finally the effect of f,ζ and the intensity of the excitation are addressed. The results show that the position of the damper relative to the rotational axis plays a significant role in determining the rotational vibration reduction, and that the LCVA is more adaptable with regards to its position relative to the structure, through the proper selection of the area of vertical to horizontal tube section ratio.