Theoretical analysis and experimental study of a nonlinear U-shaped bi-directional piezoelectric energy harvester

Narrow bandwidth and uni-directional acquisition restrict the application of a conventional cantilever piezoelectric energy harvester. In this study, a magnet-induced nonlinear U-shaped bi-directional piezoelectric harvester is proposed to overcome the shortcomings of the conventional harvester. The U-shaped harvester consists of a beam bent into a U shape with both ends fixed. A pair of piezoelectric plates is attached to the beam for power generation. To introduce nonlinear magnetic force, a magnet is attached to the center of the beam while a pair of magnets are fixed to the base. The theoretical model of the proposed harvester is developed and validated with experimental results. The proposed harvester is investigated in two orthogonal directions of vibration. The proposed harvester shows linear responses in vertical excitations. However, a strong hardening effect can be observed in horizontal excitations especially when the magnet gap is small. It is shown that the hardening effect can improve both the harvesting bandwidth and the output power in horizontal excitations. On the other hand, the resonant frequency of the vertical mode can be increased while that of the horizontal mode is decreased by reducing the magnet gap. This indicates that the magnet gap can be utilized to tune the ratio between the vertical and horizontal resonant frequencies to match the frequencies of vibration sources. Overall, the proposed nonlinear U-shaped harvester demonstrates the capability of bi-directional harvesting and improved performance with the aid of nonlinear magnetic force.