Investigation of response of systems with active multiple tuned mass dampers

Abstract

The active multiple tuned mass dampers (AMTMD), consisting of several active tuned mass dampers (ATMD), with the uniform distribution of natural frequencies have been proposed by Li et al. (J. Struct. Eng. (ASCE) 2003; 129(7):972–977) to attenuate undesirable oscillations of structures under ground acceleration. Here, the open–closed-loop AMTMDs, referred to as the OCL-AMTMD, have been further investigated including both the open-loop and closed-loop AMTMD, referred, respectively, to as the OL-AMTMD and CL-AMTMD. 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 the OCL-AMTMD is then formulated. The criterion for the optimum searching can thus be defined as the minimization of the minimum values of the maximum DMF (i.e. min.min.max.DMF). With resorting to this criterion, the research is carried out on the parameters measuring both the effectiveness and robustness of the OCL-AMTMD. The parameters include the frequency spacing, average damping ratio, tuning frequency ratio, total number, total mass ratio, and structural and seismic normalized acceleration feedback gain factor (NAFGF). Via estimating the OL-AMTMD, CL-AMTMD, and OCL-AMTMD, it is found that the CL-AMTMD and OCL-AMTMD may further enhance the performance of the multiple tuned mass dampers (MTMD) and a single open–closed-loop active tuned mass damper (referred to as the OCL-ATMD). Likewise, the near-zero optimum average damping ratio found by Li and Liu (J. Struct. Eng. (ASCE) 2002; 128(10):1362–1365) will disappear in the CL-AMTMD and OCL-AMTMD. For the OL-AMTMD, however, there yet exists the near-zero optimum average damping ratio. Copyright © 2007 John Wiley & Sons, Ltd.