Analysis of uniformly and linearly distributed mass dampers under harmonic and earthquake excitation

The effectiveness of multiple mass dampers has been investigated by Igusa and Xu [Dynamic characteristics of multiple tuned mass substructures with closely spaced frequencies. Earthq. Engng Struct. Dynam. 21 (1992) 1050–70], Yamaguchi and Harnpornchai [Fundamental characteristics of multiple tuned mass dampers for suppressing harmonically forced oscillations. Earthq. Engng Struct. Dynam. 22 (1993) 51–62], Abe and Fujino [Dynamic characterization of multiple tuned mass dampers and some design formulas. Earthq. Engng Struct. Dynam. 23 (1994) 813–35] and Kareem and Kline [Performance of multiple mass dampers under random loading. J. Struct. Engng 121 (1995) 348–61]. In this paper, we extend the results of these previous investigations to examine the performance of uniformly and linearly distributed multiple mass dampers, respectively. These systems were selected to ascertain whether the distribution of masses located close to the central mass damper would influence the performance of the entire system in reducing vibration. We evaluate performance numerically through assessing the effectiveness and robustness of each system, as well as considering the effects of redundancy, under harmonic excitation. In this regard, we evaluate the performance of the system when certain individual dampers do not function. We show that the uniformly distributed mass system is more effective in reducing the peak dynamic magnification factor. The linearly distributed system is more robust under mistuning. It is more robust to damping variation for low damping values but the effectiveness of the two systems converges as damping increases. The uniformly distributed system is slightly more reliable when an individual damper fails. The eleven mass system is optimum for both configurations for harmonic excitation. The 21-mass system is more effective in structural vibration decay in both cases for the El Centro earthquake simulation.