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The multiple tuned mass dampers (MTMDs) are considered among the control systems used for reducing the vibration of buildings under seismic excitations. A large number of the previous studies have mainly emphasized on the utilization and effectiveness of MTMD on linear structure responses, and few of them have investigated the effectiveness of MTMD on nonlinear multi-degree of freedom structures. Thus, in this paper, the effectiveness of MTMD on nonlinear buildings have been investigated. The effectiveness of the MTMD systems lies in their parameters, and the location of dampers in buildings. Accordingly, the optimization of MTMD’s properties, as well as its location, are taken into account in the present study. The Mouth Brooding Fish algorithm, which is a new optimization method is utilized for optimizing the properties corresponding to the MTMD system. The effectiveness levels of the MTMDs were compared with the efficiency of an equal optimally tuned mass damper (TMD), which was placed on the top of the building. The results of these comparisons revealed that MTMDs have provided a better efficiency compared to TMDs in reducing the maximum displacement of nonlinear structures. Moreover, MTMDs have a higher effectiveness when placed on different floors of the building.

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Some structural control systems have been devised to protect structures against earthquakes, which the tuned mass damper (TMD) being one of the earliest. The effect of a tuned mass damper depends on its properties, such as mass, damping coefficient, and stiffness. The parameters of tuned mass dampers need to be tuned based on the main system and applied load. In most of the papers, the parameters of TMDs have been tuned based on the nominal parameters of structures. Also, most of the studies considered the minimization of maximum displacement of structure as the objective function of optimizing the parameters of tuned mass dampers. In this study, according to the Monte Carlo method and using the Mouth Brooding Fish algorithm, TMDs have been optimized based on the reliability of structures regarding the uncertain parameters of buildings, and their efficiency in the reduction of maximum displacement and failure probability of hundreds generated buildings with uncertain parameters, are compared with the efficiency of the displacement-based optimized TMDs. The results show that the TMDs optimized regarding uncertainty have better efficiency in reducing the maximum displacement, and failure probability of buildings than the TMDs optimized regarding nominal parameters of buildings. Also, according to the results, the displacement-based optimized TMDs regarding uncertainty show better efficiency in reducing the failure probability and displacement of the buildings than reliability-based optimized TMDs.