Nonlinear vibration energy harvesting via parametric excitation: Snap-through with time-varying potential wells

Abstract

This study introduces a novel method to improve snap-through transitions in a parametrically excited cantilever-based energy harvester featuring repulsive magnetic coupling. The aim is to enhance the efficiency of a piezoelectric energy harvester while broadening its operational frequency range. The design incorporates an oscillating substructure that magnetically interacts with the beam, promoting easier transitions. Additionally, this setup capitalizes on the resonant energy of the substructure to optimize energy capture. This study addresses a previously unexplored limitation in the directly excited counterpart by optimizing the use of substructure’s resonant energy to significantly improve the energy harvesting device’s efficiency. We present a theoretical model based on the Hamilton principle, which is solved numerically. Comprehensive experimental studies are conducted to validate the theoretical results, showing a strong correlation between the experimental outcomes and theoretical predictions. The findings indicate that an oscillating substructure with a tailored natural frequency close to twice that of the parametrically excited piezoelectric beam can induce time-varying potential wells to facilitate snap-through transitions. Despite the damping coefficient of the piezoelectric beam being three times higher than that of its simple beam counterpart, periodic perturbations still effectively expand its instability region. This enlarged instability region, resulting from such perturbations, not only exhibits broadband characteristics but also facilitates efficient energy harvesting at lower excitation levels.