# Distributed Passive Actuation Schemes for Seismic Protection of Multibuilding Systems
## 5 Seismic Responses
Also in this case, it can be appreciated the progressive loss of performance of the configuration DC3 as we move away from the only actuated building \(\mathcal{B}^{(1)}\). Regarding the approaching peak-values, the plots in Figure 11 show that the three damping configurations are able to keep the interbuilding approaches within remarkably low levels. In fact, for the considered seismic disturbance, an interbuilding gap of 3.5 cm can be considered a safe interbuilding separation in all the cases. It is worth noting that the best approaching results are attained  
Figure 8: Full-scale 180-component of El Centro 1940 ground-acceleration seismic record with an absolute acceleration-peak of 3.417 m/s\({}^{2}\). Data available at Strong-Motion Virtual Data Center (VDC) ([[ftp://strongmotioncenter.org/vdc/smdb/1940/c/139u37](ftp://strongmotioncenter.org/vdc/smdb/1940/c/139u37) el.c0a]([ftp://strongmotioncenter.org/vdc/smdb/1940/c/139u37](ftp://strongmotioncenter.org/vdc/smdb/1940/c/139u37) el.c0a)). To gain a better understanding of the relevance of linked configurations in the seismic protection of the overall MBS, we have considered an additional unlinked damping configuration DC4 (see Figure 12), which has been obtained by removing the interbuilding dampers in the linked configuration DC2. The interstory-drift and acceleration peak-values produced by DC4 are displayed in Figures 13 and 14, respectively, and the corresponding maximum approaches are presented in Figure 15. The peak-values produced by the nonactuated MBS and the linked configuration DC2 are also included in those figures as a reference. Looking at the plots of interstory-drift peak-values in Figure 13, it can be appreciated that the unlinked configuration DC4 (red dotted lines with triangles) produces better results than the linked configuration DC2 in the actuated buildings \(\mathcal{B}^{(2)}\) and \(\mathcal{B}^{(4)}\), but it provides null protection to the nonactuated buildings \(\mathcal{B}^{(1)}\), \(\mathcal{B}^{(3)}\) and \(\mathcal{B}^{(5)}\). The plots of acceleration peak-values in Figure 14 indicate that, in addition of providing null protection to the nonactuated buildings, the unlinked configuration DC4 attains worse results than the linked configuration DC2 in building \(\mathcal{B}^{(4)}\) and the first story of building \(\mathcal{B}^{(2)}\). As to the interbuilding approaches, the plots in Figure 15 show that large approaching peak-values are produced at the top level of all the buildings by the unlinked configuration DC4, which would require interbuilding separations of about 20 cm to avoid bounding. Figure 12: Fully unlinked damping configuration DC4 obtained by suppressing the interbuilding dampers in the linked configuration DC2. Figure 13: Maximum absolute interstory drifts corresponding to the nonactuated multibuilding system (plain configuration), the linked configuration DC2 and the unlinked configuration DC4. Finally, to summarize the global behavior of the nonactuated MBS and the discussed damping configurations, we consider the overall peak-values of absolute interstory drifts  
\[|\hat{r}|_{\max}=\max_{1\leq j\leq m}\left(\max_{1\leq i\leq n}|\hat{r}_{i}^{j}|_ {\max}\right), \tag{83}\]  
absolute story total-accelerations  
\[|a|_{\max}=\max_{1\leq j\leq m}\left(\max_{1\leq i\leq n}|a_{i}^{j}|_{\max}\right) \tag{84}\]  
and interbuilding approaches  
\[(\hat{r})_{\max}=\max_{1\leq j\leq m-1}\left(\max_{1\leq i\leq n}(\hat{r}_{i}^ {j})_{\max}\right). \tag{85}\]  
The obtained overall peak-values and the corresponding \(H_{\infty}\)-norms are collected in \[(\vec{r}_{i}^{j})_{\text{max}}=\max_{0\leq t\leq T_{w}}\vec{r}_{i}^{j}(t),i=1, \ldots,5,\,j=1,\ldots,4, \tag{82}\]0 The data in the table indicate that, with respect to the nonactuated MBS, the DDS configurations DC1 and DC2 produce reductions of about 50% in the overall interstory-drift peak-value and around 40% in the overall acceleration peak-value.