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Controlling the maximum acceleration and displacement of the roof within the acceptable range is important and essential. In order to control structures, a number of control systems have been introduced that are categorized into four system including active, passive, semi active and hybrid system. One of the most used passive systems is the tuned mass damper system which is placed on the roof of structure for controlling the behavior of building. In addition, the optimization of structures subjected to the earthquake load is an essential task for the safe and economic design of structures. It must be noted that earthquakes are random phenomena and the precise prediction of forthcoming events is a hard task. However, in seismic design codes, the static and modal seismic methods for the seismic design of structures are adopted by the design spectrum produced based on previous earthquakes. Hence, in order to overcome this problem, the concept of critical excitation as a robust method has been presented and developed to generate worst–case critical excitations. The critical excitation method have been presented in the framework of an optimization problem to maximize the structural responses subjected to some constraints. In this paper, an effective method is presented to determine the optimum values for the parameters of the tuned mass damper system subjected to critical earthquakes. The critical earthquakes are unique and are computed based on the dynamical properties of the structure. For this purpose, based on the obtained information from the past occurred earthquakes the critical earthquakes of a ten story shear building are established subjected to the constraints. The constraint scenarios include some computable properties of the ground motion such as energy, peak ground acceleration an upper bound Fourier amplitude spectrum. In fact, in this stage, to compute the critical earthquakes an inverse nonlinear constraint optimization problem must be solved for each time step. Then, the building equipped by a tuned mass damper system at roof of the structure (controlled building) is considered and the optimal design of tuned mass damper subjected to critical earthquakes are implemented. The maximum absolute displacement and acceleration of the roof are considered as the objective functions. Finally, among the computed earthquakes, one of them which produces the maximum objective functions is selected as the critical earthquake. In the optimization procedure, the mass, damping and stiffness of the tuned mass damper (TMD) system are adopted as the design variables. Multi-objective particle swarm optimization method is used to optimize the parameters of the tuned mass damper system. Since, the optimal design of the tuned mass damper system is presented as a multi-objective optimization problem, a set of optimal solutions are obtained. Numerical examples demonstrate the ability and efficiency of the proposed method in the optimal design of the tuned mass damper system subjected to the critical earthquakes. In addition, the numerical results show that the maximum absolute values of the displacement and acceleration of the roof efficiently decreases when the building is controlled by the optimum tuned mass damper system. Also, the results show that the severe earthquake needs a bigger mass for tuned mass damper in order to control the displacement and acceleration of the roof.

Keywords: Critical excitation, Tuned mass damper, Multi-optimization, Particle swarm optimization method

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