# A Linear-Arc Composite Beam Piezoelectric Energy Harvester Modeling and Finite Element Analysis
## 5 Conclusions  
This paper outlines a design for a linear-arc composite beam piezoelectric energy harvester (PEH-C). The corresponding coupled governing equations were derived using the generalized Hamilton principle, laying the foundation for subsequent in-depth research. After this, the finite element simulation was performed in the COMSOL software to simulate the output voltage, stress distribution, and resonance frequency of the PEH-C under different curvatures. The impact of changes in the curvature on the PEH-C were then analyzed. Finally, the PEH-C with a curvature of 40 m\({}^{-1}\) was prepared and an experimental platform was built to verify the correctness of the relevant analysis. The following main conclusions were obtained from the simulation and experiment:  
1. The PEH-C was numerically simulated using COMSOL software to determine the relationship between the nonlinear restoring force and the transverse displacements. Then, curve fitting was performed to obtain the equation for the nonlinear restoring force. Finally, the corresponding coupled governing equations were derived by using the generalized Hamilton principle.
2. The resonance frequency of the PEH-C gradually increased with an increase in curvature. It was observed that, under the condition of keeping the length unchanged, the curvature of the curved beam part increased, the bending radius decreased, and the corresponding stiffness increased, resulting in an increase in the resonance frequency. Conversely, when the curvature was smaller, the curved beam was closer to the straight beam, the stiffness decreased, and the resonance frequency decreased accordingly.
3. Compared with the straight beam, the PEH-C introduced into the arc segment was subjected to greater stress under the same excitation. Under the same excitation, the PEH-C with a curvature of 40 m\({}^{-1}\) had the largest stress and the PEH-C with a curvature of 100 m\({}^{-1}\) had relatively uniform stress.
4. The finite element simulation results showed that the PEH-C with a curvature of 40 m\({}^{-1}\) had the best open-circuit voltage output performance. Experiments showed that the open-circuit voltage output performance of the PEH-C with a curvature of 40 m\({}^{-1}\) was 9% higher than that of the PEH-C with a curvature of 100 m\({}^{-1}\).  
Figure 16: Residency experiment.  
**Author Contributions:** Conceptualization, X.Z. and Y.G.; methodology, X.Z.; software, Y.G.; validation, X.Z., Y.G. and F.Z.; formal analysis, F.Z.; investigation, F.Z.; resources, X.C.; data curation, X.C.; writing--original draft preparation, X.Z.; writing--review and editing, X.C.; visualization, Y.G.; supervision, H.T.; project administration, H.X.; funding acquisition, H.X. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Founds of China (Grant No. 51974228 and No.51834006), the National Green Manufacturing System Integration Project (Grant No.2017-327), Shaanxi Innovative Talent Plan Project (Grant No.2018 TD-032), and Key R&D project in Shaanxi (Grant No.2018 ZDCXL-GY-06-04).  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** First of all, I would like to give my heartfelt thanks to all the people who have helped me in this paper. My sincere and hearty thanks and appreciations go firstly to my supervisor, [PERSON], whose suggestions and encouragement have given me much insight into these translation studies. It has been a great privilege and joy to study under his guidance and supervision. Furthermore, it is my honor to benefit from his personality and diligence, which I will treasure my whole life. My gratitude to him knows no bounds.  
**Conflicts of Interest:** The authors declare no conflict of interest.