## 4 Experimental Tests and Results  
A specific test rig was developed to excite by means of a hammer for modal testing a small harvester equipped with a cantilever DVA, which is a simple prototype of the harvester with ITD. Impulsive excitation instead of shaker excitation was adopted, because the testing equipment is cheaper and allows obtaining the same FRFs [35]. The harvester base was clamped at one end of a suspended aluminum bar and the hammer hit was exerted at the opposite end of the bar, see Figure 7. In this way, the hammer impact generated longitudinal vibrations inside the bar that in turn generated the base motion of the harvester. The aluminum bar was suspended from a frame by means of ropes in order to isolate the system from sources of vibrations other than the hammer impact. The pendular motion caused by the ropes showed a natural frequency about 50 times smaller than the frequencies of the harvester with DVA predicted by the analytical model, and did not influence measurements. The dimensions of the bar were selected in order to avoid the presence of bending modes of the bar in the range of frequencies of interest. Figure 5: Open circuit FRFs of the prototypes calculated by means of the analytical model. Effect of trimming frequency. Figure 6: FRFs of the prototypes with optimal resistance calculated by means of the analytical model. The measurement system included a piezoelectric accelerometer mounted on the clamped base of the harvester and a piezoelectric load cell mounted on the head of the hammer for modal testing. The signals of the sensors and the voltage generated by the harvester were acquired by means of a NI 9234 board. Digital signals were analyzed in time and frequency domain by means of NI Signal Express (Version 2015, National Instruments, Austin, TX, USA, 2015). Two electrical parameters were measured to evaluate the performance of the harvester: the open circuit voltage and the load voltage in the presence of the optimal load resistance [36]. The FRFs between open circuit voltage and base acceleration were measured in order to highlight the effect of the cantilever DVAs on harvester trimming. Five measurements were carried out in each configuration, then the mean values of resonance frequencies and peak amplitudes were calculated. The repeatability of resonance frequencies resulted in about two times the frequency resolution, which is 0.33 Hz. The repeatability of peak amplitudes resulted in about \(\pm\)5%. Figure 8a shows an example of measured results. Three configurations are considered: harvester PPA 1001 alone, harvester PPA 1001 with A1, and harvester PPA 1001 with a tip mass. As foreseen by the analytical model, the introduction of the cantilever DVA splits the original resonance peak into two new peaks, the former at lower frequency, the latter at higher frequency. Figure 8: Measured FRFs of the harvester alone, with tip mass and with cantilever DVA. **(a)** Open circuit. (**b)** Optimal load resistance. Figure 7: Testing equipment for impulsive testing. The amplitude of the first peak is slightly lower than the amplitude of the original peak, Table 2 shows that it increases if the mass of the DVA increases. The amplitude of the second peak is about 1/3 of the one of the original peak and it decreases if the mass of the DVA increases. The frequency interval (\(\Delta f\)) between the two peaks increases when the mass of the DVA increases. The comparison between Tables 1 and 2 highlights that the analytical model, which considers only one mode of vibration of the cantilever with DVA, predicts with sufficient accuracy the behavior of the harvester with DVA, therefore in the next future this simple model will be used for optimization purposes. Modal damping was calculated by means of the half-power-points method [38]. Results, which are summarized in Table 2, highlight that the damping ratio \(\zeta\) of the first mode of vibration of the coupled system is essentially equal to the one of the fundamental mode of the harvester alone.