# Snap-Through Buckling Mechanism for Frequency-up Conversion in Piezoelectric Energy Harvesting
## 4 Results
### Experimental Characterization of the STB-EH Prototypes in Open-Circuit Configuration
Conversely, for model B, the resonant frequency (\(f_{\text{res,2}}=305\,\text{Hz}\)) of the bimorph beam and the global frequencies are closer to one another, and consequently the induced oscillations and output voltage have higher amplitude. The results shown in Figures 10 and 11 refer to tests in which STB occurs from the reversed to the initial undeformed stable configurations. As explained by means of the numerical analyses, the curved beams of the bistable mechanism do not snap dynamically from the initial undeformed configuration to the reversed one and, in this situation, FuC does not occurr. The Fourier transform shown in Figure 11b is characterized, in comparison with the one shown in Figure 10b, by peaks at lower frequencies and higher values of voltage. These aspects are both due to the increase of mass caused by the presence of the lead sphere on the bimorph's free edge in model B, which causes the reduction of the global modal frequencies and the increase of the compliance of the beam. Experimental Characterization of the STB-EH Prototype Connected to a Resistive Load and to a Rectifier Circuit with Storage Capacitor  
The tests described in the previous section aim at the characterization of the STB-EH prototype in the open-circuit situation, considering the manual activation of the bistable mechanism. An additional set of experiments is devoted to the investigation of the performances in the presence of an electrical load. As before, the bistable mechanism snaps from the reversed configuration to the inital undeformed one; two kinds of external circuits are considered, namely: a resistive load and a full-wave bridge rectifier circuit connected to a storage capacitor. Model B is considered, since the experimental tests, reported in Section 4.2, confirm that it is the most promising configuration. The STB-EH prototype is characterized connecting a resistive load \(R_{\text{L}}\) to the bimorph beam. The voltage across the resistance is measured after snap occurs, and the extracted power is computed according to the Joule's law. Several experiments are executed with different attached resistances, in order to find the optimal value of \(R_{\text{L}}\) that gives the maximum value of the instantaneous power. Figure 12 shows that the instantaneous power has a maximum value of \(4\,\text{mW}\) for \(R_{\text{L}}=400\,\text{k}\Omega\), which represents the optimal value for the free vibration of the STB-EH prototype after the snap. In this situation, the average power is computed as follows:  
\[P_{\text{mean}}=\frac{V_{\text{rms}}^{2}}{R_{\text{L}}}=91.84\,\text{\mu W} \tag{4}\]  
Figure 11: Open-circuit output voltage obtained during the STB test (model B): measured time history (**a**), Fourier transform of the signals compared to the numerical outcomes (**b**). The corresponding energy, evaluated over a period of 190 ms, is 17.48 \(\upmu\)J. For the sake of comparison, the energy barrier to activate the snap from the reversed to the initial configuration can be measured in Figure 6 and it is equal to 197.76 \(\upmu\)J. Therefore, the harvested energy for a single snap is about 8.84% of the energy that is needed to activate the snap. The average power can be used to compute the power density, with respect to the volume of the active material. On an account taken of the geometric features summarized in Table 1b, one finds that the power density is 9.11 mW/cm\({}^{3}\). Such a value is in agreement with the data reported in [37], where the median power density, over a set of 29 harvesters proposed in the literature, is 5.4 mW/cm\({}^{3}\). Subsequently, the output of the bimorph beam is connected to a circuit composed of a full-wave bridge rectifier and a storage capacitor, with capacitance \(C_{\mathrm{S}}\). For the rectifier, p-n diodes 1N4148 have been used.