# A Novel Ropes-Driven Wideband Piezoelectric Vibration Energy Harvester
## 4 Results and Discussion  
The novel harvester's superior output performance and fine wideband capability were experimentally verified by comparison with the AB-VEH. In order to generate a comparative figure, the output power is normalized with respect to the active volume of piezoelectric material and (input acceleration) [4]. Figure 6 shows the frequency response of the AB-VEH system connected in parallel and series--individual beam 1, beam 2, and beam 3 resonate at 58.8, 64.4, and 69.8 Hz with normalized peak output power of 914.0 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)), 958.9 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)), and 900.7 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) under optimal load resistance of 250 k\(\Omega\), respectively. It is clearly observed that the output power decreases damply as the number of beams increase from one to three in parallel or series, which agrees with theoretical analysis. For example, when beam 1, beam 2, and beam 3 are connected in parallel, peak output power of beam 1, beam 2, and beam 3 decrease to 359.1 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)), 278.6 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)), and 329.9 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) under optimal load resistance of 85 k\(\Omega\), which are 2.7 times, 3.4 times, and 2.7 times less than that of the original single beam, respectively, and these values are close to the predicted value of 3. Further, it can be observed that the AB-VEH realizes wideband energy harvesting only by adding the number of beams with the original narrow-frequency bandwidth, and the output power still drops drastically when ambient vibration frequency is not close to the resonant frequencies of beams [6]. Figure 7 plots the normalized peak power generated by the novel energy harvester with an optimal load resistance of 40 k\(\Omega\). Seen from Figure 7, for LFDB1, LFDB2, and LFDB3 driving an  
Figure 6: Normalized output power of AB-VEH connected in (**a**) parallel and (**b**) series with optimal load resistance. HFGB individually, normalized peak output powers of the HFGB are 23.1 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) (66.5 Hz), 22.4 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) (72.5 Hz), and 24.3 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) (77 Hz), respectively; for LFDB1 and LFDB2 driving HFGB together, peak output powers of the HFGB are 23.4 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) (66.5 Hz) and 22.0 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) (72.5 Hz), respectively; for LFDB1, LFDB2, and LFDB3 driving HFGB together, peak output powers of HFGB are 23.2 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) (66.5 Hz), 21.9 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) (72.5 Hz), and 24.1 \(\upmu\)W/(mm\({}^{3}\cdot\)g\({}^{2}\)) (77 Hz), respectively, which clearly shows that the peak output powers are almost unchanged by the number of LFDB. Hence, it is possible to achieve much wider or even unlimited bandwidth with unchanged output power by adding LFDBs. In addition, the frequency response of individual LFDBs driving the HFGB has the frequency-widened-bandwidth performance. For the same frequency bandwidth environment, the novel VEH needs fewer low-frequency beams than the AB-VEH. Also, it can be seen that the output power of the novel VEH is different than the AB-VEH, which is reduced with increasing the bandwidth. It should be pointed out that the current experimental study is focused on demonstrating wideband characteristic of the proposed VEH, and the design of the novel VEH has been not optimized for practical applications in terms of output power [4] and voltage [33]. In fact, as shown later, the performances are affected by multiple parameters such as beam's stiffness and rope margin, thus better performances are expected through optimization of parameters. According to the analytical model of the wideband VEH using a stopper, in this model, certain parameters--such as input acceleration, rope margin, and stiffness of driving beam--show strong influences on the frequency response.