عنوان مقاله [English]
A passive control strategy is the use of Tuned Mass Dampers (TMD). In a simple form, the TMD consists of 1 to 10 percent of the structure effective mass connected to the main structure through a spring and a dashpot (viscous damper). The design is based on tuning the frequency of the TMD to the predominant frequency of the structure. So, when the structure is excited, the secondary mass vibrates in resonance with the structural motion, with 90 degrees of phase shift, and the TMD damping dissipates the input energy; consequently, a significant reduction in the response of the structure is achieved. Although the design process of the TMD, which includes determining its parameters, i.e., mass, stiffness and damping, is simple, finding optimum parameters has always been a challenging area in its analysis and design. In most optimization studies on tuned mass dampers, tuning and damping ratios are optimized and the damper mass is a pre-assumed parameter in design, because its optimum value is large and economically unjustifiable in real structures. In this paper, on the basis of the structure energy balance equation for a single-degree-of-freedom model and an iterative formula that tends to minimize the kinetic energy of the structure, a wise (targeted) method has been developed to find the optimum mass of the damper that reduces the maximum response of the system under harmonic and earthquake base accelerations. Eventually, good agreement was seen between the results of the present study and the ones obtained by previous related studies, which provides the possibility of optimal design of the damper through a simple iterative process. Also, the effectiveness of the optimum TMD in a nonlinear structure has been investigated. It was shown that when the structure behaves nonlinearly, the effectiveness of the TMD in reducing the peak response decreases, but, it provides damage reduction, and, for more severe input, protects the structure from collapsing compared to an uncontrolled structure.