Seismic optimization of pendulum tuned mass damper with hysteretic damping

The inherent nonlinearity of the pendulum motion becomes increasingly pronounced as excitation amplitudes rise, leading to the uncertainty of vibration and the loss of predictive accuracy owing to the linear assumption. To address this concern, this study introduces the pendulum tuned mass damper (PTMD) with hysteretic damping (HD) to realize the nonlinear performance oriented optimal seismic design. The primary contribution of this study is introducing the nonlinear performance of the PTMD with HD, thereby proposing amplitude robustness optimization based on nonlinear dynamic performance. Theoretical configurations of PTMD that facilitate different types of damping, including viscous damping (VD), constant damping, and hysteretic damping (HD), are compared. The Krylov-Bogoliubov (K-B) method is originally adopted to analyze the nonlinear effect of the PTMDs in the case of forced oscillation and free vibration. The nonlinear frequency response functions (FRFs) of the structure-PTMD system are derived, and the coupled systems are evaluated. The presence of stiffness softening, the persistence of stable solutions, and the occurrence of unstable frequency response loops demonstrate the inherent nonlinearity and sensitivity of control effectiveness. Attenuation characteristics of the PTMDs are obtained to determine the damping dissipation properties with accuracy compared with the dynamic solutions. Prue HD shows a similar dynamic interaction with an exponential decay in damping dissipation as the VD, which exhibits the linear damping performance for the coupled control system. A nonlinear performance oriented optimal seismic design based on the amplitude robustness index is proposed to consider the amplitude uncertainty impact on the structure-PTMD system. A case study is assessed based on the 20 -story benchmark structure to investigate the functionality of the proposed optimization for the PTMD with HD. The results confirm the effectiveness of optimization from the perspective of FRFs, where the optimal PTMD with HD exhibited an FRF with a lower peak in structural amplitude compared to the optimal PTMD with VD. Seismic validations of the spectral analysis and specific earthquake evaluations verify the applicability of the proposed optimization for PTMD with HD, enabling an enlarged damping dissipation capacity as earthquake excitation increases to provide better structural protection.