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Tuned mass damper (TMD) have been studied and installed in structures extensively to protect the structures against lateral loads. Multiple tuned mass dampers (MTMDs) which include a number of TMDs with different parameters have been proposed for improving the performance of single TMDs. When the structural system is considered as multiple degrees of freedom (MDOF) and implemented with MTMDs, there is no effective closed-form solution to determine the optimal parameters of MTMDs. On the other hand designing optimal MTMDs include a large number of variables. For optimal design of MTMDs, in this research an effective method has been proposed in which the parameters of TMDs are determined based on minimizing the Hankel’s norm of structure. Since the optimization procedure includes a large number of variables, hence it has been decided to use Genetic Algorithms (GAs) for determining the variables. For numerical simulation, the method has been utilized on an eight-storey shear frame modeled as MDOF, and optimal MTMDs have been designed. The results show that using the Hankel’s norm of structure as objective function has led to design effective MTMDs which could be effective in reducing the response of structure, especially the average value, under different far-field and near-field earthquakes. Also it has been found that the method is effective regarding its simplicity and convergence in solving complex optimization problem. Through extensive numerical analysis the effect of MTMDs mass ratio and TMDs number in MTMDs has been studied.

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In this research, optimal design and assessment of multiple tuned mass dampers (MTMDs) capability in mitigating the damage of nonlinear steel structures subjected to earthquake excitation has been studied. Optimal parameters of TMDs on nonlinear multi-degree-of-freedom (MDOF) structures have been determined based on minimizing the maximum relative displacement (drift) of structure where for solving the optimization problem the genetic algorithm (GA) has been used successfully. For numerical analysis, three and nine storey 2-D moment resisting nonlinear steel frames subjected to far-field and near-field earthquakes and optimal MTMDs has been designed for different values of mass ratio and TMDs number. According to the results of numerical simulations, it can be said that MTMDs mechanism could reduce the damage of nonlinear steel structures where the effectiveness increases by increasing TMDs mass ratio. Also the performance of MTMDs depends on earthquake characteristics, mass ratio and TMDs configuration where in this research the effective case has been locating TMDs on top floor in parallel configuration.

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The main focus of this research has been to investigate the effectiveness of optimal single and multiple Tuned Mass Dampers (TMDs) under different ground motions as well as to develop a procedure for designing TMD and MTMDs to be effective under multiple records. To determine the parameters of TMD and MTMDs under multiple records various scenarios have been suggested and their efficiency has been assessed. For numerical simulations, a ten-story linear shear building frame subjected to 12 real earthquakes as well as a filtered white noise record and optimum parameters of TMDs and MTMDs have been determined by solving an optimization problem using genetic algorithm (GA). The results show that when designing optimal TMD and MTMD under a specific ground motion, using the optimization procedure leads to achieve the best performance while the characteristics of the design earthquake strongly affects the performance of TMDs. Furthermore, it has been found that TMDs and MTMDs designed using only one earthquake as the design record have not worked successfully under multiple ground motions. For determining the parameters of TMDs to be effective under multiple records it has been suggested to use the mean of optimal TMDs parameters obtained using each of the design records.

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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.