Optimal design of tuned liquid column damper inerter for vibration control

In this paper, the use of a novel passive control device defined as Tuned Liquid Column Damper Inerter (TLCDI) is studied to control the seismic response of structural systems. The TLCDI, recently introduced as an enhanced version of the conventional Tuned Liquid Column Damper, may achieve improved seismic performances by exploiting the mass amplification effect of the so-called inerter device. For this purpose, an optimization procedure for the design of the TLCDI based on a statistical linearization technique and the minimization of the structural displacement variance is proposed. Notably, by assuming a white noise base excitation and considering some additional approximations, pertinent closed-form expressions for the optimal TLCDI parameters are provided. The reliability of the proposed analytical solutions is proved by a comparison with numerical results obtained by a more computationally demanding iterative optimization technique on the original damped system. Finally, the efficiency of the control performance of TLCDI-controlled structures is examined using real recorded seismic signals as external excitation.