# Elasto-Plastic Short Exoskeleton to Improve the Dynamic and Seismic Performance of Frame Structures
## 7 Conclusions  
In this paper, a 2-DOF model, representing a general N-DOF frame structure, was coupled with an external yielding 1-DOF system, representing an exoskeleton, to improve the dynamic and seismic behaviour of the 2-DOF model. A rigid link connects the bottom mass of the 2-DOF model to the 1-DOF yielding system. Such a yielding system was assumed to have an elasto-plastic constitutive behaviour that was modelled by the Bouc-Wen model. Due to the rigid link between the 2-DOF model of the structure and yielding system, the coupled system was still described by a 2-DOF mechanical model. The nonlinear equations of motion were obtained by a direct approach and successively numerically integrated to analyse the dynamics of the coupled system. The coupling with the yielding system was considered beneficial for the structure in the occurrence of a reduction in the displacements and drifts of the structure. An extensive parametric analysis was performed, considering both harmonic and seismic excitations. The parameters varied in the analysis were those characterising the elasto-plastic constitutive behaviours of the yielding system. The results were summarised in behaviour maps that provided the ratios between the maximum displacements (or the drift) of the coupled system and the stand-alone structure. In these maps, a ratio less than unity shows that the yielding system is effective in improving the dynamics of the structure. The analysis showed wide regions of the parameter plane where the coupling is beneficial for the structure. In correspondence of the points of the maps where the best performances occur, the yielding system exhibits a behaviour with hysteretic cycles that have a high value of equivalent damping coefficient. As expected, the performance of the coupled system also depends on its characteristics and on the spectral content of the excitation. Since, in all cases, the coupling with the yielding system is beneficial for the sub-structure, the coupling may be particularly effective in structures with the so-called soft storey, which is usually located at the lower levels of structures. The coupling can reduce the displacement of such storeys up to 90% of their initial values and, at the same time, could improve the dynamic and seismic performances of the super-structure. The results encourage checking the effectiveness of such a method for real structures by using more accurate FEM models. However, the results reveal that if the frame structure to be protected is sufficiently regular, the used low-dimensional models can properly capture the dynamic and seismic behaviour of the structure. Finally, the main novelties and advantages of the study are summarised below:  
* Differently to the use of braced and/or knee-braced frames that are usually distributed in the whole structure, the proposed method uses an exoskeleton that involves only a small part of the structure to be protected. * Since the connection between the structure and the exoskeleton is performed by rigid links at the level of the first (or second) storey, the mechanical and geometric characteristics of the structure to be protected remain unchanged. * Although the exoskeleton is shorter than the frame structure, it has the ability to improve the dynamic and seismic response of both the part below the connection with the exoskeleton and the part above such a connection. * The stiffness and the mass of the exoskeleton are parameters that can be varied easily and that can be used to improve the performances of the coupled system. This possibility is harder to exploit in braced and/or knee-braced frames. On the contrary, the proposed method has the following limitations:
* The exoskeleton requires some space around the frame structure to protect and could have an undesired aesthetic impact. * The limited height of the exoskeleton may undermine the effectiveness of the proposed protection for high-rise buildings.