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A tuned mass damper inerter (TMDI) is a new class of passive control device based on the inclusion of an inerter mechanism into a conventional tuned mass damper (TMD). The inerter device provides inertial resisting forces to the controlled system, through relatively small masses, converting it in a mechanism with the potential to enhance the performance of passive energy dissipating systems. This work presents a study of an optimal TMDI design through an exhaustive search process. TMDI device design using the cited parameter selection methodology consists in the determination of the damper critical damping ratio, ζTMDI, and frequency ratio, υTMDI, which result in the minimum structural response of a multidegree of freedom structural system, considering predefined values for mass ratio (µ) and inertance ratio (β). The used optimization process examines all possible damping device design parameter combinations to select the set of values that results in the best device performance to reduce response parameters in a structure. Four different optimization processes are performed by independently minimizing four performance indices: J1 associated to the reduction of the structure’s maximum peak displacement, J2 calculates the minimal RMS value for the structure’s peak displacement, J3 seeks by the minimal peak interstorey drift, and JP determines the lowest value for a linear weighted combination of the abovementioned three indices. A numerical example is developed with the purpose of validating the proposed optimization procedure and to evaluate the benefits of using TMDI as controlling devices for structures under seismic excitation, by carrying out a comparative analysis to contrast the performance of the optimization alternatives developed, running up to 1968192 cases. The obtained results show that devices designed based on exhaustive search optimization produce peak displacement reductions of up to 35% and peak structure displacement RMS reductions of up to 30%.

Design of a Tuned Mass Damper Inerter (TMDI) Based on an Exhaustive Search Optimization for Structural Control of Buildings under Seismic Excitations