# Trapezoidal Cantilevers with Irregular Cross-Sections for Energy Harvesting Systems
## 4 Experimental Investigation of Modified Trapezoidal Cantilevers
The analysis of Figure 16a revealed that a cantilever with trapezoidal gaps has the best response to the base excitation. Considering cantilever base widths, \(L_{B3}\) (Table 1), it could be concluded that trapezoidal gaps have a positive influence on the base excitation response of the system. These gaps reduced the stiffness of the cantilever, and thus, the response characteristic was improved. Furthermore, the generated voltage from the unit of the piezo ceramic volume was chosen as a criterion to compare cantilevers from the view point of open circuit voltage density. Figure 16b reveals that a cantilever with trapezoidal gaps has the best open voltage density characteristic. This is caused by gaps that reduced the cantilevers' stiffness and improved strain in the piezo ceramic. Figure 15: Experimental setup: 1,2, optical displacement sensor; 3, plastic clamping frame; 4, computer; 5, power amplifier; 6, function generator; 7, electromagnetic shaker; 8, variable resistive load; 9, micro current probe; 10, oscilloscope. The open circuit voltage density of the modified cantilever has a 3% higher value in comparison with the conventional beam. The output voltage density tip displacement characteristics for each cantilever were measured. The output voltage was measured by the oscilloscope Yokogawa DL2000 (Yokogawa, Tokyo, Japan). Variable resistance load was attached in parallel to the piezo ceramic. The tip displacement was controlled by optical sensors. The results of the investigation are given in Figure 17.  
Graphs of Figure 17 show that modified cantilevers have higher values of output voltage density. Therefore, it can be concluded that modifications of the cross-section area have a positive influence on the electrical characteristics of the cantilevers. Comparing the maximum values of output voltage density, it can be seen that the output voltage density of modified cantilevers was increased up to 9.9% compared to the conventional cantilever (Figure 18). Considering this, it can be concluded that modification of the cross-section can ensure higher output voltage density. Moreover, such modifications ensure more effective piezo ceramic employment. The output current density versus tip displacement were measured for each cantilever, as well. Current was measured by a micro current probe that employs the Burden voltage phenomenon. The probe was connected to the oscilloscope, and the values were recorded. The results of the investigation are given in Figure 19.  
Figure 16: Cantilever response and open circuit voltage density characteristics: (**a**) displacement characteristics; (**b**) open circuit voltage density characteristics. Table 3.0 Output voltage density tip displacement characteristics: (**a**) conventional cantilever; (**b**) with cylindrical gaps; (**c**) with trapezoidal gaps. The results of the measurements showed that output current density was improved for cantilevers with a modified cross-section. Considering the results, it could be concluded that modifications of the cross-section area have a positive influence on the output current density. Comparing the maximum values for the output current density, it can be noticed that cross-section modifications increased output current density up to 6.9% in comparison with the conventional cantilever (Figure 20). According to the results of this investigation, it can be concluded that the energy conversion coefficient was improved by modifications of the cross-section area. The comparison of the power density was made for each cantilever, as well. Such a comparison reveals the efficiency of each cantilever beam. Electrical power at 1 M\(\Omega\) with the tip displacement of 100 \(\upmu\)m was chosen as a critical parameter. The results are presented in Table 3.1 A cantilever with cylindrical gaps has the best power density of 8.8 \(\upmu\)W/mm\({}^{3}\). This power density value is 3.14-times higher in comparison with the conventional cantilever.