To investigate the coupling effects between the internal resonance and nonlinear magnetic interaction for multi-directional 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.

为了研究多向能量收集的内部共振和非线性磁相互作用之间的耦合效应，本研究提出了一种单压电悬臂-非线性磁摆结构。所提出的结构主要由压电悬臂梁、固定在梁自由端的磁摆和摆下方的基座永磁体组成。内部共振是由二维空间中的钟摆运动与共振时的梁弯曲振动之间的非线性耦合引起的。磁摆和基础磁铁之间的磁性相互作用引入了非线性。所提出的结构经过理论建模和实验实现，以证明其能量收集能力。x方向的能量收集比传统的压电悬臂-摆系统宽三倍。同时，所提出的结构还实现了额外的内部谐振频率范围（3.4 Hz–4.3 Hz），以提高z方向的能量收集性能。在所研究的频域中，所提出结构的实验最大功率输出在 7.5 Hz 时达到 0.64 mW。