Simplified analytical solution for the optimal design of Tuned Mass Damper Inerter for base isolated structures

In this paper the use of the Tuned Mass Damper Inerter (TMDI) to control the response of base isolated structures under stochastic horizontal base acceleration is examined. Notably, the TMDI, recently introduced as a generalization of the classical Tuned Mass Damper, allows to achieve enhanced performance compared to the other passive vibration control devices. Thus, it represents an ideal alternative for reducing displacements of base isolated structures. To this aim, firstly a straightforward numerical approach is developed for the optimal design of this device considering a white noise base excitation. Further, a simplified analytical solution for the optimal design of TMDI parameters for base isolated structures is proposed minimizing the displacement variance of the corresponding undamped base isolated system. A thorough numerical analysis is performed and related results, in terms of optimal parameters and control performance, are compared with pertinent data obtained by a more computationally demanding iterative optimization procedure on the original damped system, considering both white noise and coloured noise stationary base excitation. Analytical and numerical results are found in good agreement, especially in terms of control performance, thus establishing the reliability and efficiency of the proposed approach. Finally, numerical analyses on a five-story benchmark base isolated structure controlled with an optimally designed TMDI are performed considering real recorded ground motions as base excitation. It is concluded that the TMDI, properly optimized with the proposed procedure, can effectively reduce the response of base isolated structures even under strong earthquakes.