## 4 Experimental Tests and Results
The FRFs of Figure 8a show that harvester with cantilever DVA has two modes of vibration that can be excited by a uniform distribution of base acceleration. Conversely, even if the range of frequency of the FRF is extended, harvester PPA 1001 alone shows only a very small peak at 763 Hz caused by the excitation of the second bending mode. From the point of view of trimming, the cantilever DVA is able to lower the frequency of the main resonance peak by some tens of Hz. It should be noted that the same effect of the cantilever DVA can be obtained by means of a tip mass. Figure 8a shows that with a tip mass of 0.591 g (much larger than the one of A1) the natural frequency is roughly equal to the first natural frequency of PPA 1001 equipped with A1. With this solution the generated voltage is larger, but the stress inside the piezoelectric material increases as well. The same series of measurements was carried out considering for each harvester configuration the optimal load resistance for the first resonance peak at frequency \(\omega_{r}\), which is given by Equation (15). Figure 8b shows an example of the experimental results. In all the cases here considered the amplitudes in resonance are significantly lower than the ones in open circuit condition due to the effect of the resistance [6]. The resonance frequency of PPA 1001 and of PPA 1001 with tip mass slightly decreases passing from the open circuit condition to the optimal resistance condition; this result is in agreement with [6; 37] and the analytical results. In the harvester equipped with DVA the introduction of the optimal resistance lowers the frequency of the first resonance peak by about 1 Hz and has a very small effect on the frequency of the second peak. Therefore, the frequency shifts caused by the cantilever DVAs in the presence of optimal load are similar to those of Table 2.  
The power (\(P\)) generated by the harvester in resonance can be calculated from the voltage (\(V_{L}\)) measured in loaded condition:  
\[P=\frac{V_{L}^{2}}{2R_{opt}}=\frac{|FRF_{L}|^{2}a_{bb}^{2}}{2R_{opt}} \tag{16}\]  
\(FRF_{L}\) is the FRF measured in loaded condition. If base acceleration \(a_{bb}\) is set to 10 ms\({}^{-2}\), harvester PPA 1001 generates in resonance 1.61 mW, whereas harvester PPA 1001 with A1 generates 0.97 mW at the first resonance and 0.37 mW at the second resonance. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**1 st Mode**} & \multicolumn{4}{c}{**2 nd Mode**} \\ \cline{2-9}
**Harvester** & \begin{tabular}{c} **Frequency** \\ **\(f_{1}\) (Hz)** \\ \end{tabular} & \begin{tabular}{c} **Peak** \\ **Amplitude** \\ **(V/ms\({}^{-2}\))** \\ \end{tabular} & \begin{tabular}{c} **Damping** \\ **Ratio \(\zeta\)** \\ \end{tabular} & \begin{tabular}{c} **Frequency** \\ **\(f_{2}\) (Hz)** \\ \end{tabular} & \
\begin{tabular}{c} **Peak** \\ **Amplitude** \\ **(V/ms\({}^{-2}\))** \\ \end{tabular} &
\begin{tabular}{c} **Damping** \\ **Ratio \(\zeta\)** \\ \end{tabular} & \(\Delta F\) **(Hz)** \\ \hline PPA 1001 & 126.4 & 1.85 & 0.0072 & - & - & - & - \\ PPA 1001 + Tip & 90.0 & 2.48 & 0.0087 & - & - & - & - \\ MAss & & & & & & \\ PPA 1001 + A1 & 88.2 & 1.35 & 0.0087 & 158.9 & 0.55 & 0.0085 & 70.7 \\ PPA 1001 + A2 & 93.2 & 1.33 & 0.0080 & 156.4 & 0.61 & 0.0077 & 63.2 \\ PPA 1001 + A3 & 97.4 & 1.25 & 0.0073 & 148.3 & 0.79 & 0.0071 & 50.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Resonance frequencies of the coupled systems and corresponding amplitudes of the prototypes. Mean values of five tests.