## 9 Conclusions  
This paper aims to evaluate the performance of the TMD, TMDI, and the pendulum PTMD to reduce excessive vibrations in a 42-story hybrid timber building. The outcomes of the study are summarized as follows. * A proposed robust pendulum PTMD with the same mass ratio as TMD and TMDI offers an excellent vibration reduction due to its superior energy dissipation at the bounding boundary. Under earthquake excitations, the proposed device can reduce the peak displacement at the top floor by 19.5%, while the TMD reduces the same response by 11.9%, and the TMDI reduces the response by 4.1%. In addition, the pendulum PTMD reduces top floor acceleration by 11%, while the TMD reduces it by a negligible amount. The robustness of the pendulum PTMD is superior compared to TMD/TMDI. * The pendulum PTMD reduced the base shear force by 55.7% (STD) and 14.5% (peak value), the base moment by 41% (STD) and 14% (peak value), and the maximum inter-story drift ratio by 40% (peak value). The superior performance of the proposed pendulum PTMD in reducing peak accelerations reveals that the device can minimize damage to the building's nonstructural elements (pipes, ceiling, partitions, etc.) during seismic events. * An equivalent TMD, including the physical mass of the inerter, is proposed for a one-to-one performance comparison between TMD and TMDI. The introduction of the inerter in a linear TMD may change the optimal device properties (damping ratio and tuning frequency, resulting in reduced energy dissipation). The results show that the equivalent  
Figure 24: The bounding force under El-Centro earthquake excitation. TMD is better than TMDI in minimizing the building responses under variable frequency sinewave excitations unless the mass ratio is significantly small (<0.005). * The three devices can minimize acceleration better (compared to displacement) under filtered white noise (wind loads). However, the opposite is true under a variable frequency sinewave excitation (earthquake excitation). Nevertheless, due to the nonlinear behavior of the pendulum PTMD, higher modes are controlled, which results in a higher reduction in the acceleration response. * The control capabilities of the TMD increase with the increase in the mass ratio. However, the responses are sensitive to small mass ratios (0-2%). Similarly, for a given mass ratio, the vibration reduction capabilities of the TMDI increase as the inertance ratio increases. The structural responses are sensitive to the inertance ratio within the range of 0-0.5. Increasing the inertance ratio beyond 0.5 is inefficient and increases the device's physical mass. * Pendulum PTMD has a potential application against multi-hazard (wind/earthquake) loads, resulting in sustainable and resilient future infrastructures. It can address the challenges of physical civil infrastructure to be resilient and sustainable over its service lifetime, under service and long-term conditions, including increased demands due to climate change adaptation and other emerging stressors (including single and multiple hazard events). The dominant capabilities of this novel device in a timber-hybrid building under different excitations reveal benefits that can shape the future of the physical infrastructure and contribute to climate change adaptation and mitigation for improved disaster resilience. In addition, these findings can contribute to fostering community welfare and promoting environmentally friendly, circular economy policies. Conceptualization, A.M.A. ; Methodology, S.C. and A.M.A. ; Writing--original draft, S.C. and A.M.A. ; Funding acquisition, A.M.A. All authors have read and agreed to the published version of the manuscript. The second author ([PERSON]) received funds from the Louisiana Board of Regents (ITRS program: LEQSF(2022-25)-RD-B-02), Louisiana State University (LSU) NSF I-Corps, LSU Faculty Grant, as well as LSU Economic Development Assistantships (EDAs) through the NSF EPSCoR program. The findings are those of the authors and do not necessarily represent the sponsors' views.