Optimization of non-uniformly distributed multiple tuned mass damper

A gradient-based method for optimizing non-uniformly distributed multiple tuned mass damper (MTMD) is presented in this paper. By solving an optimization problem with multiple objectives, optimized non-uniformly distributed MTMDs are obtained. Then the dynamic characteristics, effectiveness, robustness and redundancy of MTMDs are investigated in detail. Without restrictive assumptions such as uniformly distributed frequency, identical damping ratio, the optimized non-uniformly MTMDs obtained here can be considered as the “true” optimal ones. Unlike the references [L. Zuo, S.A. Nayfeh, Optimization of the individual stiffness and damping parameters in multiple-tuned-mass–damper system, Journal of Vibration and Acoustics—Transactions of the ASME 127(1) (2005) 77–83; N. Hoang, P. Warnitchai, Design of multiple tuned mass damper by using a numerical optimizer, Earthquake Engineering and Structural Dynamics 34(2) (2005) 125–144], the maximum displacement or frequency response of the main structure is chosen as the objective function in the present paper, because the maximum displacement is more concerned than the root-mean-square response sometimes. Using the presented method, the errors of estimate of the parameters of the structure and the MTMD can be taken into account quantitatively in the design procedure of the MTMD. It is demonstrated that the MTMDs designed in this paper are more effective than the traditional optimal uniformly distributed MTMDs whose frequency spacing, stiffness or mass and damping are under some restrictions for simplicity. And the MTMDs designed by accounting for possible errors of estimate are more robust than those without consideration of errors.