Optimal tuning of tuned liquid column damper systems in random vibration by means of an approximate formulation

Passive control devices are often added to slender and flexible systems in order to increase their structural safety. Several types of devices have been proposed in order to reduce the dynamic responses of different kind of structural systems. Among them, the tuned liquid column damper (TLCD) proved to be very effective in reducing vibration of various type of structures by means of a combined action which involves the motion of the liquid mass within the tube. The restoring force, in particular, is produced by the force of gravity acting on the liquid and the damping effect is generated by the hydrodynamic head losses that arise during the motion of the liquid inside the TLCD. Since the increasing use of TLCD in practical realizations, an approximated simplified formulation, by means of a statistical linearization technique has been previously developed by the same authors. This direct and ready-to-use formulation is able to predict the effectiveness of TLCD on a structure subjected to random loads and has been numerically validated by means of a parametric analysis in a stochastic framework by comparison with the numerical Monte Carlo simulation based on the nonlinear complete system for a wide range of the system parameters. In this paper optimal TLCD parameters have been computed taking advantage of the proposed approximated formulation, by which a smooth function, defining the main system variance, can be formulated and easily minimized, resulting in a significant reduction of the computational time and a valuable tool for design purposes. Moreover, starting from the proposed formulation, optimal design charts have been created which enable for an easy and quick evaluation of the TLCD parameters design.