Viscous dampers (VDs) are effective and widely used passive devices for the protection of civil structures, provided that appropriate design is carried out. For this purpose, optimal design and optimum distribution of VDs method are presented for a shear building under the critical excitation by using random vibration theory in the frequency domain. In the optimization, by using Differential Evolution (DE) algorithm and the top floor displacement are evaluated as objective functions taking into consideration upper and lower limits of VDs damping coefficients, so that optimal damper placement and properties of the shear building can be determined. In this design, the VDs-shear building system is tested under the three different ground motions being compared to some methods in the literature and uniformly distributed VDs placed at each story. It is shown that the results of the study are both compatible and very successful in reducing the response of the structure under the different ground motions.

Tuned mass damper (TMD) is an effective passive device in reducing harmful vibrations as long as they are designed correctly. An optimal TMD design method is proposed based on transfer functions and also differential evolution (DE) algorithm is used. The method includes optimization of all parameters which are the mass, stiffness and damping coefficients of a TMD. By using random vibration theory, the mean-square of top floor absolute acceleration, top floor displacement and the sum of mean-squares of interstorey drifts have been chosen as objective functions to be minimized with respect to upper and lower limits of TMD parameters. In the classical design, the mass is usually chosen by the designer to find the optimum values of the stiffness and damping coefficient. In addition to optimizing stiffness and damping coefficients, in this study TMD mass quantity is also optimized by using DE algorithm to minimize objective functions for TMD design. After that, structure system with TMD is tested under six near fault and three far fault ground motions by evaluating responses of the structure. The results obtained here are compared with the methods available in the literature for verification. Numerical results show that the proposed method is effective for optimal TMD design.