Effects of tuned mass dampers on the modal response characteristics of discrete structures

Tuned Mass Dampers (TMDs) are efficient passive control devices that effectively mitigate structural vibrations. However, when multiple TMDs are used for multimodal control, they may cause modal deviations in the primary structure, thereby reducing their effectiveness in vibration control. Furthermore, traditional mode-by-mode design approach cannot account for the synergistic effects between TMDs, thus leading to suboptimal design outcomes. This study focuses on a two-degree-of-freedom(2DOF) discrete structure and proposes an optimization design method based on the synergistic effects between TMDs. The proposed method is compared with the traditional mode-by-mode approach through numerical examples. Subsequently, a complex modal analysis is conducted to investigate the modal deviation characteristics of the primary structure under optimal design parameters. Finally, seismic time history analysis is conducted to evaluate the vibration mitigation effects of each TMD and their interactions. The results show that the proposed method can achieve better control performance with a lower damping ratio of TMD2 (control Mode 2) compared to the traditional mode-by-mode design approach. The TMD with a large mass ratio does not affect the frequency or mode shape of the 2DOF discrete structure, but it significantly increases its modal damping ratio. Under the optimal design parameters, both TMD1 (control Mode 1) and TMD2 effectively reduce the peak and root mean square (RMS) responses of the primary structure. When both TMD1 and TMD2 control the first two modes of the primary structure, TMD2 does not affect the tuning performance of TMD1 but reduces its operational efficiency. This effect becomes more pronounced as the mass ratio of TMD2 increases.