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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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In recent years, semi-active control has been introduced as a promising method for the seismic control of structures, potentially combining the benefits of both passive and active control systems. Magneto-rheological damper (MR) is one of the semi-active devices and its dynamic model is expressed by the Bouc-Wen model. The sliding sector control (SSC) strategy as a robust control approach is a class of variable structure (VS) systems for linear and nonlinear continuous-time systems with a special type of sliding sector using a new equivalent sector control. The purpose of this study is to evaluate the effectiveness of the SSC strategy in determining the optimal voltage of MR at each step of time. For a numerical example, a three-story benchmark shear structure is considered subjected to normal (100%), high (150%), and low (50%) excitation levels of the El Centro earthquake. The results of the numerical simulations show that the semi-active control system consisting of the SSC strategy and an MR damper can be beneficial in reducing the seismic responses of structures. Furthermore, the efficiency of the SSC strategy is also compared against that of the fuzzy and clipped-optimal controllers. Comparative results of the numerical simulation confirm the robustness and ability of the SSC strategy.