Effective and Robust Vibration Control Using Series Multiple Tuned-Mass Dampers

Various types of tuned-mass dampers (TMDs), or dynamic vibration absorbers, have been proposed in literature, including the classic TMD, (parallel) multiple TMDs, multidegree-of-freedom (DOF) TMD, and three-element TMD. In this paper we study the characteristics and optimization of a new type of TMD system, in which multiple absorbers are connected to the primary system in series. Decentralized $H2$ and $H∞$ control methods are adopted to optimize the parameters of spring stiffness and damping coefficients for random and harmonic vibration. It is found that series multiple TMDs are more effective and robust than all the other types of TMDs of the same mass ratio. The series two TMDs of total mass ratio of 5% can appear to have 31–66% more mass than the classical TMD, and it can perform better than the optimal parallel ten TMDs of the same total mass ratio. The series TMDs are also less sensitive to the parameter variance of the primary system than other TMD(s). Unlike in the parallel multiple TMDs where at the optimum the absorber mass is almost equally distributed, in the optimal series TMDs the mass of the first absorber is generally much larger than the second one. Similar to the 2DOF TMD, the optimal series two TMDs also have zero damping in one of its two connections, and further increased effectiveness can be obtained if a negative dashpot is allowed. The optimal performance and parameters of series two TMDs are obtained and presented in a form of ready-to-use design charts.