## 8 Conclusions  
Analytical calculations and experimental results show that it is possible to develop cantilever DVAs that behave as reactive mechanical loads and that are able to modify the natural frequencies and modes of vibration of the harvester, without significantly increasing the damping of the system.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Harvester** & \(L\) **(mm)** & \(be\) **(mm)** & \(bc\) **(mm)** & **Frequency (Hz)** & **Peak Power (mW)** & \(\sigma\) **(MPa)** \\ \hline PPA 1001 & 40.1 & 20.8 & 20.8 & 124.5 & 1.42 & 55 \\ PPA + ITD1 & 40.1 & 20.8 & 20.8 & 89.3 & 1.10 & 37 \\ PPA + ITD2 & 40.1 & 20.8 & 20.8 & 89.5 & 0.95 & 33 \\ PPA + tip mass & 40.1 & 20.8 & 20.8 & 87.3 & 2.33 & 85 \\ Slender-rectangular & 48.8 & 17.5 & 17.5 & 87.6 & 1.95 & 70 \\ Inverse tapered & 41.1 & 31.6 & 10.0 & 87.4 & 2.30 & 118 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dimensional characteristics of the zirconate/lead titanate (PZT) layer, generated power ad maximum stress of PPA 1001 and various harvesters trimmed to the same frequency, base acceleration is 10 ms\({}^{-2}\).  
Usually, vibration energy is available at frequencies lower than the fundamental frequency of a piezoelectric harvester. Experimental results show that decrements in the fundamental frequency of about 30% can be achieved by means of a simple cantilever DVA.  
These concepts, which have been validated by means of prototypes built with a simple technology, are then extended to develop the ITDs. The integration of the trimming device with the structural layer of the harvester is a promising technology, since the extension of the structural layer (steel or plastic material) would be rather inexpensive and the extension could be cut into the desired shape by means of consolidated technologies, such as punching or laser cutting. The harvester with ITD appears simpler and cheaper than other promising solutions.  
In the framework of this research the potentialities of harvesters equipped with ITDs have been investigated by means of FE simulation. Numerical results show that the ITDs basically have the same properties of the cantilever DVA, but some different designs are possible, which correspond to different performances of the harvester.  
The first integrated trimming device (ITD1) is suited to lower the natural frequency of the harvester of about 35 Hz and to collect power at low frequency (1.1 mW). The second integrated trimming device (ITD2) is characterized by two resonance peaks with multiple frequencies and it is suited to collect energy from periodic excitation.  
The main limit of an ITD seems the increased length of the device, but this limit could be overcome with a folded design in which the mass lies near the harvester base.  
Future research directions are testing and numerical simulation of harvesters equipped with more complex ITDs, which behave as dynamic systems with many DOFs.  
The research was carried out in the framework of the research program: \"Piezoelectric micro-electro-mechanical power supply for automotive wireless sensors\" funded by University of Padova--Italy grant CPDA142798.  
[PERSON] with the contributions of [PERSON] and [PERSON] conceived of the trimming devices; [PERSON] and [PERSON] performed the experiments; [PERSON] performed the simulations with the supervision of [PERSON]; [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] analyzed and discussed the results, and revised the paper written by [PERSON].  
The authors declare no conflict of interest.