Internal resonance characteristics of a bistable electromagnetic energy harvester for performance enhancement

This paper explores the internal resonance characteristics of a bistable electromagnetic vibration energy harvester (BEEH) and utilizes the feature to achieve energy harvesting enhancement. Two linear natural frequencies are tuned to meet the nearly commensurate ratio, i.e., 1:2. The frequency spectra are introduced to demonstrate the mode coupling and energy exchange between the first two modes. With small excitation amplitudes, only intra-well responses are obtained, and the energy exchange between modes obeys the commensurate relation when the excitation frequency equals the first linear natural frequency, i.e., 1:2. However, it does not obey the ratio when the inter-well responses are activated, and the energy transfers to several other modes, which results in chaotic inter-well responses. Afterward, the bifurcation diagrams and basin-ofattraction maps are implemented to gain insights into the nonlinear responses of the BEEH, which quantitatively demonstrate the dominance of the chaotic responses. An intriguing phenomenon is that almost all dynamic responses become chaotic under large excitation amplitude regardless of initial conditions. Finally, comparisons between the tuned BEEH model and a mistuned model are conducted. The results elucidate that the internal resonance characteristic enhances the vibration energy harvesting performance in terms of both the bandwidth and the power output compared to the mistuned system.