Optimum Design of Pendulum Tuned Mass Dampers Considering Control Performance Degradation from Damper Connection

Pendulum tuned mass dampers (PTMDs) are one of the most commonly used devices for high-rise structures to control large-amplitude vibrations due to dynamic excitations. In practice, the damper of PTMD usually connects the tuned mass to the location below the top floor rather than to the top floor, which is different from the case using a conventional tuned mass damper (TMD). Therefore, the classical optimal parametric formulas derived from the structure-conventional TMD model are not applicable to design the optimal parameters of PTMDs. In this paper, the simplified mechanical model of the structure-PTMD system is updated to consider the damper connection in practice. The fixed-points theory is employed to analytically derive the optimum design formulas for the PTMD by introducing the effect of modal shape. Moreover, the control effectiveness of the PTMD using the proposed method is studied. The control performance and robustness of the PTMD designed by the proposed method are compared to those designed by the classical optimum formulas under various dynamic loads. Finally, with the help of the performance degradation index (PDI), the control performance degradation of PTMD designed by classical formulas is quantified. The results show that the proposed optimal parameters have considerable differences from classical formulas. Through designing a PTMD on a multi-degree-of-freedom (MDOF) structure, the proposed optimum design is demonstrated to be more effective and robust than the classical formulas. To design a large mass ratio PTMD, the control performance degradation from the damper connection in practice is significant and should be seriously considered.