Minimax optimization of multi-degree-of-freedom tuned-mass dampers

Many methods have been developed for the design of a single-degree-of-freedom (SDOF) absorber to damp SDOF vibration. Yet there are few studies for the case where both the absorber and the main system have multiple degrees of freedom. In this paper, an efficient numerical approach based on the descent-subgradient method is proposed to maximize the minimal damping of modes in a prescribed frequency range for general viscous or hysteretic multi-degree-of-freedom (MDOF) tuned-mass systems. Examples are given to illustrate the efficiency of the minimax method and the damping potential of MDOF tuned-mass dampers (TMDs). The performance of minimax, H2, and H∞ optimal TMDs are compared. Finally, the results of an experiment in which a 2-DOF TMD is optimized to damp the first two flexural modes of a free–free beam are presented.