Interplay between internal resonance and nonlinear magnetic interaction for multi-directional energy harvesting

To investigate the coupling effects between the internal resonance and nonlinear magnetic interaction for multidirectional energy harvesting, this study proposed a single piezoelectric cantilever-nonlinear magnetic pendulum structure. The proposed structure was mainly composed of a piezoelectric cantilever beam, a magnetic pendulum fixed at the free end of the beam, and a base permanent magnet below the pendulum. Internal resonance was induced by the nonlinear coupling between the pendulum motion in the two-dimensional space and the beam bending vibration at resonance. The magnetic interactions between the magnetic pendulum and the base magnet introduced nonlinearity. The proposed structure was theoretically modeled and experimentally realized to demonstrate its energy harvesting capabilities. Owing to the positive coupling effects between the internal resonance and nonlinearity in the proposed structure under the properly chosen parameters, the experimental results showed that the internal resonance bandwidth of the proposed structure for the x-direction energy harvesting was three times wider than that of the traditional piezoelectric cantilever-pendulum system. Meanwhile, the proposed structure also achieved an additional internal resonant frequency range (3.4 Hz-4.3 Hz) for improving the z-direction energy harvesting performance. The experimental maximum power output of the proposed structure achieved 0.64 mW at 7.5 Hz in the investigated frequency domain.