Multi-directional cantilever-spring-pendulum by considering the telescopic magnet–spring oscillator for enhancing the performance of energy harvesting

Abstract Harvesting energy from vibrational environments to power wireless sensors has significant potential. This paper proposes a multi-directional cantilever-spring-pendulum by considering a telescopic magnet–spring oscillator. The proposed structure demonstrated adaptability to low-frequency vibrational environments. By incorporating a spring oscillator configuration, the external energy is nonlinearly transferred via magnetic forces to the piezoelectric cantilever-spring pendulum system. Moreover, under multi-system coupling, vibrational energy from multiple directions can be effectively converted into electrical energy, enabling multidirectional energy harvesting. The governing equations of the system are derived by establishing a magnetic dipole model to formulate the magnetic energy equation, in combination with the Lagrange’s equations. The simulation results indicate that the proposed spring oscillator provides additional excitation energy, the peak RMS voltage is increased under z -direction excitation, and the energy harvesting bandwidth is broadened under x -direction excitation. Modeling analysis and simulation demonstrate that with appropriate parameter configurations, the spring oscillator structure significantly enhances energy harvesting performance. In conclusion, compared with the traditional pendulum-type energy harvester, the peak RMS voltage of the proposed structure increased by 40.13% in z -direction, and its operational frequency bandwidth could be increased by more than 94.99% in x -direction. In addition, the maximum RMS voltage was 3.72 V under z -direction excitation and 3.98 V under x -direction excitation.