Multiple Poincare sections approach in an example energy harvesting system with time-varying potential

This paper presents a comprehensive numerical analysis of a nonlinear energy harvesting system utilizing magnetic interactions and piezoelectric transducers. The primary objective of the study was to evaluate the influence of varying magnetic pole configurations and excitation parameters on the system's energy efficiency. For the configuration exhibiting the most favorable energy properties, a detailed dynamic analysis was conducted, considering the presence of coexisting solutions and regions of chaotic excitation. Special emphasis was placed on an original identification procedure for multiple Poincaré sections, based on partitioning phase coordinate sequences into even and odd sets. The analysis revealed complex phenomena, such as transient chaos and the coexistence of multiple stable periodic orbits, which – under specific initial conditions – offer significantly higher energy effectiveness than standard solutions. The results confirmed that the optimal magnet configuration ensures stable energy harvesting over a wide frequency range, while the number of excited multiple Poincaré sections is significantly determined by the cyclic variation of the potential.