# Energy Harvester Based on a Rotational Pendulum Supported with FEM
## 5 Conclusions  
This paper investigates the dynamic response of an electromagnetic energy harvester with a rotational pendulum with variable magnetic-force interactions. Based on the concept proposed in [7] with a simplified model, in this work a more rigorous two-stage mathematical model is proposed that includes FEM analysis of magnet-magnet and magnet-coil couplings. The governing equation of motion is presented, which includes the magnetic interaction terms from FEA from the first stage. Based on a physically realized model built using the 3D printing method, physical quantities and terms in the mathematical model were obtained. In this investigation, three majorly different cases were tested, which were configurations with and without coils and magnet couplings, and with adjustable magnet positions. The findings from the constant amplitude excitation experiments highlighted the significant impact of magnetic force on the pendulum's traversal through the magnetic barriers. When larger magnets were employed in a repulsive setup, the pendulum more easily overcame the initial barrier. Furthermore, as the pendulum exited the magnetic field of additional magnets, it experienced a substantial acceleration, which contributed to the increased kinetic energy. This heightened energy level enabled the pendulum to navigate through the subsequent magnetic barriers more effectively. The results suggest that optimization of the system should involve strategically adjusting the position and strength of repulsive or attractive magnets for a fine tuning of the potential landscape. By doing so, nonlinearities will dominate the dynamics of the pendulum and enhance energy harvesting efficiency. Additionally, a comprehensive understanding of the system's behavior requires investigations on various initial conditions and excitation frequencies. Future works involving such analyses will reveal a spectrum of potential operating regimes, each offering advantages in terms of energy harvesting capabilities. By delving into these aspects, novel strategies for improving the rotational pendulum-based energy harvesting systems can be explored, thereby broadening the practical applications. In our next step, a comprehensive investigation of the model under different angular and axial positions of the side magnets is to be carried out. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14083265/s1](https://www.mdpi.com/article/10.3390/app14083265/s1)]([https://www.mdpi.com/article/10.3390/app14083265/s1](https://www.mdpi.com/article/10.3390/app14083265/s1)), Figure S1: **(a)** Global mesh model of a stationary pendulum and magnet-coil pair. **(b)** Local enlarged mesh view of a stationary pendulum and a magnet-coil pair. **(c)** Contours of magnetic flux density [T] at a distance of \(-27.5\) mm along x-axis; Figure S2: Variation of components of magnet force in x, y, and z axes with the distance between the magnets along x-axis are shown in **(a-c)**, respectively; Figure S3: Under the application of 1A current through coil, variation of components of magnet force in x, y, and z axes with the distance between the magnets along x-axis are shown in **(a-c)**, respectively; Figure S4: **(a)** Local mesh of a quasi-dynamic model for a pendulum-magnet and a coil with induced voltage. **(b)** Induced voltage in coil for different speeds of the pendulum. **(c)** Reference characteristics of induced voltage obtained  
Figure 10: Phase portraits of the considered cases **(a–c)** for the solutions shown in Figure 8a–c. after normalizing with speed; Table S1: List of variables used for the FEA simulation of magnetic force interactions. Conceptualization, G.L., M.K., P.W., B.A. and A.M.G. ; methodology, G.L., M.K., P.W., B.A. and A.M.G. ; software, G.L., M.K. and B.A. ; validation, G.L. and M.K. ; formal analysis, G.L. ; investigation, G.L. and B.A. ; resources, B.A. ; data curation, G.L., M.K., P.W. and B.A; writing--original draft preparation, G.L., B.A. and A.M.G. ; writing--review and editing, G.L., B.A.