Performance Enhancing of Galloping-based Piezoelectric Energy Harvesting by Exploiting 1:1 Internal Resonance of Magnetically Coupled Oscillators

In this study, we introduced 1:1 internal resonance in a magnetically coupled 2-degree-of-freedom (2-DOF) galloping-based piezoelectric energy harvester to improve the energy harvesting efficiency. The governing equations for the proposed magnetically coupled aero-electro-mechanical system considering the effect of oscillating wake are established using the extended Hamilton principle, and the method of multiple scale is exploited to obtain approximate analytical solutions. Parameter sweeping numerical calculation is conducted to validate the analytical prediction through comparing with analytical solutions, and the results show a good matching between them. In addition, we investigated the systematic dynamic behaviors under a pure oscillating wake induced 1:1 internal response. Typical nonlinear characteristics such as jump, hysteresis, frequency synchronization under varying design parameters appear in the present system. Especially, cusp bifurcation and synchronization regime of oscillating wake coupled nonlinear oscillator in \(\eta - {\Theta _w}\) plane and \(\sigma - {\Theta _w}\) plan. With an adoption of magnetic force, chaos happens as the gap distance decreases smaller than 5 mm, and a frequency lock-in phenomenon can be strengthened through adjusting the magnet distance. In the perspective of output performance, both of the voltage and power output results shows that the exploiting of 1:1 internal resonance can significantly improve the output performance under a suitable magnet distance.