## 5 Experimental Results
### Dynamic Tests
In addition, for the non-segmented structure, by increasing the input intensity, it was observed that the modes identified had well-spaced frequencies and modest decreases, whereas the damping factors had only a modest increase, evidencing that the four-story frame structure was within the elastic range and behaved linearly; the results are not reported for sake of brevity. For the FTMD configuration, the dynamic properties at some different input intensities are evidenced in Table 4, where natural frequencies and damping factors for the six modes  
Figure 9: WN. FTMD configuration, force displacement cycles of the isolators: (**a**) WN01 = 0.002 g, (**b**) WN05 = 0.008 g, (**c**) WN12 = 0.025 g.  
identified are estimated. It is possible to notice that the first two frequencies decrease by increasing the intensity, whereas the subsequent ones have only a modest decrease. By observing damping factors instead, it can be noticed that the first one increases with the intensity while the second one decreases. In the subsequent modes, damping factors vary with the amplitude, but in minor way, always increasing, with the exception only of the third mode. Figure 10a,b show, for the FTMD configuration, the variation in the first two frequencies, \(\mathrm{f_{1}}\) and \(\mathrm{f_{2}}\), and damping factors, \(\mathrm{\eta_{1}}\) and \(\mathrm{\eta_{2}}\), respectively, versus the RMS value of the base acceleration in the whole range investigated. In each sub-figure, the discrete values represent those experimentally identified, and the continuous curves instead represent their interpolations. By observing Figure 10a, the softening behavior introduced by the nonlinear TMD emphasized by the decrease in the first two frequencies is evident, which maintains a difference between them that is almost constant by increasing the excitation. The two curves have a regular trend and decrease with the intensity, maintaining almost the same distance between them. The first and second frequency tend to the limit values of 2.2 and 4.4 Hz, respectively, for the maximum intensity applied. The first frequency of the compared uncontrolled cases (dotted lines f1-f4 and f1-F35 in Figure 10a) are always contained in the variation frequency range of the two frequencies in the controlled case. Considering the damping factors (Figure 10b), it is possible to observe the high dissipative capabilities induced by the HDRBs. The first damping factor increases with the intensity, reaching the limit value of 13.4%, whereas the second one decreases and tends to the limit value of 5.6%. A rapid exchange of damping between the two modes, which moves from the second to the first one, is observed by increasing the excitation. The energy transfer is evident between the two controlled modes, even if the mean value between them estimated at the various intensities maintains almost the same for both modes (in mean varying the intensity indicated by \(\mathrm{\eta_{mean}}\) Figure 10b \(\approx\) 9-10%). The importance of appropriately setting modal damping by a TMD system in order to achieve its efficiency is analytically treated in [26]. In addition to white noise tests, increasing and decreasing sine sweep tests were conducted for the dynamic characterization of the three-story structure equipped with a non-conventional TMD. A typical time history registered by one accelerometer placed along the structure for increasing and decreasing SS test is depicted in Figure 11. When the SS passes through the resonance frequencies of the structure, a rapid increase in the response is observed. By taking the maxima and knowing the variation in the excitation frequency, it is possible to estimate the structural resonances directly from the time histories.