Optimum parameters of tuned mass damper for damped main system

A tuned mass damper (TMD) is a device consisting of small damped spring-mass system attached to a vibrating main system in order to attenuate any undesirable vibrations. In this paper, optimum parameters of TMD system attached to a viscously damped single degree-of-freedom main system are derived for various combinations of excitation and response parameters. The excitation applied to the main system consists of external force and base acceleration modelled as Gaussian white-noise random process. Using numerical searching technique, the optimum damping and tuning frequency ratio of the TMD are obtained for minimization of various mean square responses such as relative displacement, velocity of main mass and force transmitted to the support. The optimum parameters of the TMD system and the corresponding response quantities are obtained for different damping ratios of the main system and the mass ratios of the TMD system. Explicit formulae for damper damping, tuning frequency and the corresponding minimized response are then derived using curve-fitting technique that can be conveniently used for applications in dynamical systems. The error in these expressions is found to be negligible and hence these expressions are convenient for use in damped single degree-of-freedom main system. The optimum damping ratio of the TMD is not much influenced by the damping of the main system. However, the optimum tuning frequency of TMD is significantly affected by the damping of main system. Lastly, a comparison of the optimum damping and tuning frequency of the TMD under filtered white-noise and white-noise excitation is also made. Copyright (c) 2006 John Wiley & Sons, Ltd.