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In the area of semi-active control of civil structures, Magneto-Rheological (MR) damper has been an efficient mechanism for reducing the seismic response of structures. In this paper, an effective method based on defining an optimization problem for designing MR dampers has been proposed. In the proposed method, the parameters of semi-active control system are determined so that the maximum response of structure is minimized. To solve the optimization problem, the Genetic algorithm (GA) has been utilized. The modified Bouc-Wen model has been used to represent the dynamic behavior of MR damper while to determine the input voltage at any time step, the clipped optimal control algorithm with LQR controller has been applied. To evaluate the performance of the proposed method, a ten-storey shear frame subjected to the El-Centro excitation and for two different kinds of objective functions, optimal MR dampers have been designed. Then the performance of optimal MR damper has been tested under different excitations. The results of the numerical simulations have shown the effectiveness of the proposed method in designing optimal MR dampers that have the capability of reducing the response of the structures up to a significant level. In addition, the effect of selecting a proper objective function to achieve the best performance of MR dampers in decreasing different responses of structure has been shown.

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