# Elasto-Plastic Short Exoskeleton to Improve the Dynamic and Seismic Performance of Frame Structures
## 6 Seismic Excitation  
A set of four earthquake records is used as excitation for the seismic analyses. The selection of the records is performed accounting for the differences in the spectral characteristics of the earthquake records. The limited number of earthquake records does not directly allow assessing the sensitivity of the results on the features of the records but provides a significant indication about the ability of the exoskeleton to improve the seismic performance of frame structures. Figure 9 shows the time-histories of the selected records in the left column and the corresponding pseudo-acceleration elastic spectra on the right column. The considered earthquake records are  
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2. Kobe, Takarazuka-000 station, ground motion recorded during the 1995 Japan earthquake;
3. L'Aquila, IT.AQV.HNE.D.20090406.013240.X.ACC station, ground motion recorded during the 2009 Italian earthquake;
4. Pacoima, Dam-164 ground motion recorded during the 1971 San Fernando, California earthquake;
5. Parkfield, CO2-065 ground motion recorded during the California earthquake 1966. In the following, each record is called with the underlined name of the above list. In this case, the results are obtained by numerically integrating the equations of motion (Equation (1)). Discussion of the Results  
The first seismic analysis considers the structure whose geometric and mechanical characteristics are reported in the first rows of Tables 1 and 2, i.e., the three-storey frame structure. For this structure, the range of the main periods of the coupled system is approximately 0.32-0.39 s, as for the analysis with harmonic excitation. As shown in Figure 10a, the coupling with the yielding system is performed at the first storey of the structure. Both the \(\alpha_{1}\) and \(\alpha_{2}\) gain maps are reported in Figure 10b. When the coupled system is excited by the four records, the coupling reduces the displacements of the sub-structure. The gain index \(\alpha_{1}\) reaches values of about 0.1, which means a reduction of \(u_{1}\) of about 90% with respect to the stand-alone structure. As occurs for the harmonic excitation, also under seismic excitation, the \(\alpha_{2}\) maps present points with absolute minima. The position of these points and the corresponding values of \(\alpha_{2}\) vary with the records. Nevertheless, for all records, there is a reduction in the drift of the coupled system. For example, for the Kobe earthquake, for which the coupling is less effective, the minimum value of \(\alpha_{2}\) is about 0.66, which entails about a 30% reduction of the drift compared to the stand-alone structure. Figure 9: Time-histories and acceleration response spectra of the earthquakes analysed: (**a**) Kobe; (**b**) L’Aquila; (**c**) Pacoima; (**d**) Parkfield. Figure 11 shows the time-histories of \(u_{1}(t)\) and \(\Delta u(t)\) together with the hysteretic cycle. Such curves refer to the point labelled with \(A\) in the Pacoima maps of Figure 10. The comparison between the time-histories of the coupled system (thick line) and those of the stand-alone structure (thin line) shows a notable reduction in both the displacement of the sub-structure and the drift of the super-structure due to the coupling. Moreover, the hysteretic cycle in Figure 11 clearly shows the yielding of the system and the consequent energy dissipation. Figure 10: Gain maps: (**a**) Geometrical coupling scheme; (**b**) Gain maps \(\alpha_{1}\) and \(\alpha_{2}\) for different earthquakes (\(\psi=0.1\), \(\gamma=0.1\)). Point \(A\) denotes a reference case examined in the analyses. The last seismic analysis considers a structure whose geometric and mechanical characteristics are reported in the second row of Table 1 (six-storey building). Figure 12 shows only the \(\alpha_{2}\) maps because also in this case, the coupling is always beneficial for the sub-structure. The results refer to three different earthquakes records (Kobe, L'Aquila, and Parkfield).