# 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  
Figure 7 shows the experimental setup adopted to characterize the STB-EH prototypes (specifically, model B is shown in the figure, but the same setup is used also for the other tests). Voltage is measured by means of probes connected to an oscilloscope and to the electrodes of the bimorph beam. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(f_{1}[Hz]\) & 235 & \(f_{7}[Hz]\) & 1193 \\ \hline \(f_{2}[Hz]\) & 482 & \(f_{8}[Hz]\) & 1407 \\ \hline \(f_{3}[Hz]\) & 628 & \(f_{9}[Hz]\) & 1792 \\ \hline \(f_{4}[Hz]\) & 694 & \(f_{10}[Hz]\) & 2139 \\ \hline \(f_{5}[Hz]\) & 729 & \(f_{11}[Hz]\) & 2943 \\ \hline \(f_{6}[Hz]\) & 737 & \(f_{12}[Hz]\) & 2950 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Eigenfrequencies model A (no tip mass). \begin{table}
\begin{tabular}{c c c c} \hline \hline \(f_{1}[Hz]\) & 51 & \(f_{7}[Hz]\) & 737 \\ \hline \(f_{2}[Hz]\) & 187 & \(f_{8}[Hz]\) & 1130 \\ \hline \(f_{3}[Hz]\) & 303 & \(f_{9}[Hz]\) & 1789 \\ \hline \(f_{4}[Hz]\) & 609 & \(f_{10}[Hz]\) & 2134 \\ \hline \(f_{5}[Hz]\) & 695 & \(f_{11}[Hz]\) & 2679 \\ \hline \(f_{6}[Hz]\) & 729 & \(f_{12}[Hz]\) & 2721 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Eigenfrequencies model B (tip mass). Firstly, the resonant frequencies of the bimorph beams for models A and B are estimated by measuring the open-circuit voltage subsequent to a mechanical impulse. To this purpose, the device is clamped in a vice with the exception of the bimorph beam which is let free to oscillate due to an imparted mechanical impulse to the vice. Figures 8 and 9 show the Fourier transform of four repeated measurements of the open-circuit output voltage of the piezoelectric cantilever beam of models A and B, respectively. Figure 8: Fourier transform of the open-circuit output voltage for the computation of the resonant frequency of the bimorph beam without tip mass (model A). Figure 7: Experimental setup for model B. The peaks in the spectra correspond to the resonant frequencies of the piezoelectric cantilever beams, \(f_{\text{res,1}}^{\text{exp}}=1850\,\text{Hz}\) and \(f_{\text{res,2}}^{\text{exp}}=305\,\text{Hz}\) for models A and B, respectively. The analytical values of the resonant frequencies, computed according to the well-known formula valid for cantilever beams, are \(f_{\text{res,1}}^{\text{analyt}}=2056\,\text{Hz}\) and \(f_{\text{res,2}}^{\text{analyt}}=325\,\text{Hz}\) for models A and B, respectively. The overestimate of the analytical values is attributed to the fact that the bimorph beam is not perfectly clamped and that the actual mechanical and geometrical parameters of the beam may slightly differ from the ones employed for the computation. Subsequently, the numerical analyses described in Section 4.1 are verified by different series of tests. In particular, the open-circuit output voltage arising from the oscillations induced by STB, which is triggered by manually displacing the bistable mechanism from the reversed to the initial undeformed configuration, is measured. Figures 9(a) and 9(a) show the measured open-circuit output voltage obtained with the model A and model B, respectively. The Fourier transform of four repeatead measurements for model A and model B are shown in Figures 9(b) and 9(b), respectively. The curves are characterized by two peaks for both models, which correspond to the two first global modes, namely those involving the motion of both the bistable mechanism and the bimorph beam. Figures 9(b) and 9(a) also show the comparisons between the numerical and experimental results. In particular, a satisfactory agreement is obtained, both in terms of frequency and magnitude. With reference to model A, the resonant frequency (\(f_{\text{res,1}}=1850\,\text{Hz}\)) of the bimorph beam is higher than the two global modal frequencies and is hence far from being directly excited.