Design of Tuned Mass Damper under Bounded Uncertain Parameters Bijan Kumar Roy PG Student Bengal Engineering and Science University, Shibpur INDIA bijan.roy@rediffmail.com Bijan kumar Roy,born 1982, received his civil engineering degree from Bengal Engineering and Science University, Shibpur 2006. Rama DebBarma Research Scholar Bengal Engineering and Science University, Shibpur INDIA r.debbarma@rediffmail.com Rama DebBarma, born 1972, received her engineering degree from T. E. College, Tripura University in 1994 and Master of Engineering from B.E.College, Deemed Univ. in 2001. Subrata Chakraborty Professor Bengal Engineering and Science University, Shibpur INDIA schak@civil.becs.ac.in Subrata Chakraborty, born 1968, received his civil engineering degree from the B. E. College Univ. of Calcutta in 1991 and M.Tech and Ph.D. from IIT Kharagpur in 1993 and 1997. In general his research interest lies in computational structural mechanics Summary The tuned mass damper parameters optimization in random vibration framework considering uncertain but bounded type system parameters that includes mass, damping and stiffness of the structure as well as ground motion parameters is studied here. Though, the damper parameters optimization under uncertain parameters in probabilistic framework is powerful, the approach can not be applied in many real situations when the required detailed information on the statistical variations of the parameters is limited. In such case, the interval method is a viable alternative. With the aid of matrix perturbation theory using first order Taylor series expansion and interval extension of the dynamic response function, the problem under interval parameters is transformed here into appropriate deterministic optimization problems. Numerical study is performed to elucidate the effect of parameters uncertainties on the optimization of damper parameters. Keywords: Vibration Control, tuned mass damper, earthquake, bounded parameter uncertainties 1. Introduction One of the most important design issues is the TMD parameter optimization. The optimal design of TMD assuming deterministic system parameters are well developed. A major limitation of the deterministic approach is that the uncertainties in the performance-related decision variables cannot be included in the optimization process even when the necessary information is available. But, the efficiency of TMD may be drastically reduced if the parameters are off tuned to the vibrating mode it is designed to suppress due to unavoidable presence of uncertainty in the system parameters. Thus, in recent years, the vibration control problem of structures with uncertain parameters has attracted a great deal of interest. Though, the probabilistic methods are powerful, the approach can not be applied in many real situations when the required detailed information on the statistical variations of the parameters is limited. In such case, the convex models and interval analysis methods in which bounds on the magnitude of uncertainties are only required is a viable alternative. The present study deals with the design of TMD to minimize the safety of structure under random earthquake considering uncertainties in system parameters. The uncertain parameters include mass, damping and stiffness of the structure as well as the ground motion parameters. With the aid of matrix perturbation theory of dynamic response using first order Taylor series expansion and interval extension of the function, the TMD parameters design problem under UBB variable is transformed into appropriate deterministic optimization problems. The structural displacement is assumed as the performance index to minimize the probability of failure of the primary structure. Numerical study is performed to elucidate the effect of parameters uncertainties on the optimization of TMD parameters and overall safety of the structures.