Active Multiple Tuned Mass Dampers: A New Control Strategy

Abstract

Active multiple tuned mass dampers (AMTMD) consisting of many active tuned mass dampers (ATMDs) with uniform distribution of natural frequencies have been, for the first time here, proposed to attenuate undesirable oscillations of structures under the ground acceleration. The MTMD in the AMTMD is manufactured by keeping the identical stiffness and damping and varying the mass. In light of the physical principle of the passive MTMD, the active control forces of AMTMD are defined, namely, the control forces are generated through keeping the identical displacement and velocity feedback gain and varying the acceleration feedback gain. Based on the modegeneralized system in the specific vibration mode being controlled (referred to as the main system), the expression for the dynamic magnification factor (DMF) of the structure with AMTMD is formulated. The criterion for the optimum searching can then be defined as the minimization of the minimum values of the maximum DMF (i.e., Min.Min.Max.DMF). With resorting to the criterion, the research is conducted on the parameters reflecting the effectiveness and robustness of AMTMD. The parameters include the frequency spacing, average damping ratio, tuning frequency ratio, total number, total mass ratio, and normalized acceleration feedback gain coefficient. For the sake of comparison, the results of the optimum MTMD (the passive counterpart of AMTMD) and ATMD are also taken into account in the present paper. It is shown that AMTMD can remarkably improve the performance of the MTMD and also has higher effectiveness than ATMD. Additionally, evaluation is performed on the stroke displacement of AMTMD through assessing the maximum DMF of every ATMD in the AMTMD with regard to that of corresponding TMD in the MTMD and ATMD. Numerical results indicate that every ATMD in the AMTMD has different maximum stroke displacement, each of which is larger than that of ATMD, and the maximum stroke displacement of every ATMD in the AMTMD is close to that of corresponding TMD in the MTMD.