## 5 Conclusions  
This paper explores the feasibility of designing a seismic protection system based on a vibro-impacting nonlinear energy sink. In contrast to the existing literature, the vibro-impacting mass was positioned on an external structure with limited height, and it was connected to the first story of the frame structure to be protected. The coupled system is represented by a low-dimensional structural model with only three degrees of freedom. The mechanical characteristics of the reduced model were determined using a dynamic equivalence procedure that was previously developed by one of the authors of this paper. Given that this paper primarily focuses on an initial feasibility assessment of the proposed protection system, a simplified, ideal model that assumes an instantaneous impact was employed for the vibro-impacting mass. Figure 8: Gain maps of the coupled frame structure excited by the Kobe, Newhall, and Pacoima earthquakes (Frame 1, \(\eta=0.1\), \(r=0.7\)). A comprehensive parametric analysis was conducted involving variations in several parameters that characterize the external structure, the vibro-impacting mass, and the frame structure intended for protection. Three earthquake records were employed to excite the structure. The seismic effectiveness of coupling with the proposed protection system was evaluated using two gain coefficients, which were defined as the ratio between the displacements of the coupled and uncoupled frame structures. Values below unity for these coefficients indicated an advantage in using the proposed protection system. The results of the parametric analyses were presented in gain maps, thereby illustrating the contour plots of the gain coefficients in specific parameter planes. The results obtained from the frame structure coupled with the proposed protection system were compared to those achieved using a protection system with a fixed (non-vibro-impacting) mass. The comparison aimed to clarify the performance of the vibro-impacting mass. The findings revealed that the vibro-impacting mass effectively reduced the displacement of both the connected story and the superstructure in contrast to the protection system with a fixed mass. In the specific scenario considered, it was feasible to reduce the displacements of the connection story by an additional 20% compared to a structure without a protection device. More notably, there was a significant reduction in the drift of the superstructure, a benefit not observed when the vibro-impacting mass was not taken into account. Increasing the mass of the vibro-impacting nonlinear energy sink demonstrated effectiveness in safeguarding both the connection story and the superstructure, each in distinct ways. The augmentation in mass resulted in an additional 10% reduction in displacements for the connection story. Simultaneously, it extended the advantage region for the superstructure. Furthermore, the analyses demonstrated the relation between the effectiveness of the vibro-impacting mass and the restitution coefficient, as well as the stiffness of the external structure. A decrease in the restitution coefficient led to an expansion of the advantage regions but only to a limited reduction of the gain coefficients. An increase in the stiffness ratio between the external structure and the first story of the frame structure generally resulted in a decrease in the value of the gain coefficients. A judicious selection of these two parameters enabled the optimization of the proposed protection system's performance. The effectiveness of the proposed protection system was constrained by opting to limit the connection height to the first floor of the frame structure. This decision was driven by considerations of both aesthetics and economics. However, future studies focusing on taller structures could explore the relationship between the efficacy of the proposed protection system and the height of the connection.