An internal resonance piezoelectric energy harvester based on geometrical nonlinearities

This study investigates the effects of nonlinear modal interactions on a piezoelectric energy harvester, specifically focusing on the absence of externally induced magnetic nonlinearities. While multi-mode vibration energy harvesters aim to utilize multiple resonance regions to broaden the effective frequency bandwidth, weak nonlinear dynamic behaviors can occur with small excitations, leading to the dominance of linear behavior in the system's response. To overcome this limitation, researchers have extensively explored nonlinear techniques like magnetic couplings. However, this study demonstrates that even without external magnetically induced nonlinearities, nonlinear modal interactions can significantly impact the performance of a piezoelectric energy harvester. The device has been designed, fabricated, and subjected to testing, both an approximate analytical method and a numerical method were employed to predict and qualitatively analyze the experimental results. The findings indicate that, when the natural frequency ratio of the first two modes of the system becomes nearly commensurable, the nonlinearities of the system become more prominent as the excitation levels increase. This leads to more noticeable interactions between the nonlinear modes, ultimately resulting in an internal resonance between the first two modes. The observed phenomena, such as double-jumps and resonance energy transfers between the coupled modes, contribute to broadening the overall bandwidth and enhancing the efficiency of utilizing piezoelectric effects.