## 5 Experimental Results
### Seismic Effectiveness  
The seismic effectiveness of the structure equipped with a non-conventional TMD was with the four natural earthquake signals of characteristics reported in Table 3, applied at increasing intensity. The three configurations were tested. A first comparison was made between the responses obtained with the FTMD configuration and the F4 configuration. In order to represent synthetically the performance obtained with the use of the TMD in comparison with the non-segmented structure, the following response indices, \(J_{n},~{}n=1-6\), evaluated from the maximum values of each response quantity in the FTMD configuration normalized with the respect the same quantity in the F4 configuration, were defined:  
\[ \begin{split} J_{i}=\frac{\max[abs\left(A_{i,FTMD}\right)]}{\max[ abs\left(A_{i,F4}\right)]}~{}i=1,2,3,~{}J_{4}=\frac{\max[abs\left(D_{3,FTMD}\right)]}{ \max[abs\left(D_{3,F4}\right)]},\\ J_{5}=\frac{\max[abs\left(T_{b,FTMD}\right)]}{\max[abs\left(T_{ b,F4}\right)]},~{}J_{6}=\frac{\max[abs\left(M_{b,FTMD}\right)]}{\max[abs\left(M_{b, F4}\right)]}\end{split}  \tag{1}\]  
where \(A_{i}\) represents the acceleration at the \(i\)-level, \(D_{3}\) is the relative displacement at the third level, \(T_{b}\) is the base shear, and \(M_{b}\) is the base moment. Figure 14: SS. FTMD configuration, detail in the increasing frequency range 1–6 Hz: (**a**) first mode of the FTMD configuration, (**b**) first mode of the F3S configuration, (**c**) second mode of the FTMD configuration. Top: modal displacements vs. structure height; center: TMD and support displacement time history; bottom: force displacement cycles of the HDRB isolators. In the same manner, the response indices \(I_{n},\;n=1\)-6, evaluated from the RMS values of each response quantity in the FTMD configuration normalized with the respect the same quantity in the F4 configuration, were defined:  
\[ \begin{split} I_{i}=\frac{\text{RMS}\left(A_{i,FTMD}\right)}{ \text{RMS}\left(A_{i,F4}\right)}\;i=1,2,3,\;I_{4}=\frac{\text{RMS}\left(D_{3 FTMD }\right)}{\text{RMS}\left(D_{3 FT4}\right)},\\ I_{5}=\frac{\text{RMS}\left(T_{3 FTMD}\right)}{\text{RMS}\left(T_{ 5,F4}\right)},\;I_{6}=\frac{\text{RMS}\left(M_{3 FTMD}\right)}{\text{RMS}\left( M_{b,F4}\right)}\end{split}  \tag{2}\]  
Note that indices that have values lower than the unity imply the effectiveness of the control system in reducing the structural response in terms of RMS and peak values. The response indices evaluated at different intensities are reported in Figures 15 and 16 for near-field and far-field earthquakes, respectively. Considering the Kobe earthquake, in Figure 15a it can be shown that the indices evaluated in terms of peak values at first increase and then decrease with the PGA. Since the F4 configuration behaves linearly, these results highlight the nonlinear behavior of the structure controlled with a non-conventional TMD. All the indices have values lower than the unity, demonstrating the effectiveness of the TMD in reducing the structural responses. The reduction observed from the floor accelerations through indices \(I_{1}\), \(J_{2}\), and \(J_{3}\) increases with the height, with percentages of reductions in the range of 60-75%. Concerning the displacement reduction, index \(J_{4}\) modestly varies with the PGA, showing a reduction around 75%. Base shear and base moment, \(J_{5}\) and \(J_{6}\), have the same trend versus the PGA and show reductions of 75-80%. The indices evaluated in terms of RMS values modestly increase with the PGA and generally have higher reductions compared to the corresponding ones evaluated in terms of peak values. The accelerations, indices \(I_{1}\), \(I_{2}\), and \(I_{3}\), have percentages of reductions of 75-85%, whereas displacement, base shear, and base moment, \(I_{4}\), \(I_{5}\), and \(I_{6}\), have reductions from 85% to almost 90%. In Figure 15c,d, for the Northridge earthquake, a similar trend of the response indices in terms of peaks and RMS values versus the PGA is observed.