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To improve the behavior of building structures subjected to lateral loads, such as wind and earthquake excitations, tuned mass damper (TMD) has been used extensively theoretically and experimentally in previous researches. To increase the effectiveness of TMD mechanism, different methods have been proposed to determine the optimal values of TMD parameters including its mass, stiffness and damping. In using single TMD on the structures subjected to external vibrations, the mistuning of TMD, variation of TMD damping and changes in structural dynamic characteristics cause significant reduction in the effectiveness of TMD. Multiple tuned mass dampers (MTMDs) have been proposed to overcome the shortcomings of single TMD where each TMD has different dynamic characteristics. Based on the results of different researches, it has been concluded that the performance of MTMDs is less sensitive to uncertainty of structural dynamic parameters than that of a single TMD. In the previous researches, for designing MTMDs on the linear structures subjected to various external excitations, several methods have been proposed based on different kinds of design criteria. In most of the proposed methods, to simplify the design procedure of MTMDs, some limitations such as identical masses and damping ratios for TMDs or uniform distribution for the frequency or damping of TMDs have been considered. Also these methods require extensive numerical analysis. To generalize the design problem of MTMDs, in this paper, an effective method has been proposed for optimal design of MTMDs on the multi-degree-offreedom linear structures subjected to any desired excitation. In this method, an optimization problem is defined for designing the optimal MTMDs. The minimization of the maximum displacement of structure is considered as objective function and the parameters of TMDs are considered as variables. Since the design problem includes a large number of variables, hence, in this paper, it has been decided to use Genetic Algorithm (GA) for solving the optimization problem. To illustrate the procedure of the proposed method and also to assess the effectiveness of MTMDs in improving the seismic behavior of structures, a ten–storey linear shear building frame was subjected to white noise excitation and for different values of TMDs mass ratio and TMDs number, optimal MTMDs were designed for minimizing the maximum displacement of structure. To focus on the main objective of this paper and avoid the complexity of the problem, TMDs were located on the top floor in parallel configuration. The results of numerical simulations showed the capability of GA in solving complex MTMDsdesign problem with a large number of variables as well as the simplicity of the method under any desired external excitation. Also it was concluded that increasing of the mass ratio of TMDs could improve the effectiveness of MTMDs. To assess the performance of optimal MTMDs under other earthquakes, which are different in characteristics with design record, optimal structure-MTMDs was tested under near-fault and far-fault earthquakes and the results have been reported.

Keywords: optimization, passive control, Tuned Mass Damper (TMD), Multiple Tuned Mass Damper (MTMD)

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