Broadband energy harvesting by nonlinear magnetic rolling pendulum with subharmonic resonance

Nonlinear systems may exhibit secondary resonances, which can provide an additional and thus broadened bandwidth for energy harvesting. However, the secondary resonances of nonlinear energy harvesters reported in the literature suffer from low-power output and limited bandwidth. This work proposes a novel magnetic rolling pendulum (MRP) with a large bandwidth and high power output in both primary and secondary resonances for energy harvesting. The MRP employs the rolling motion of a magnetically levitated permanent magnet with minimal mechanical damping. A prototype was fabricated and characterised. An analytical model combined with finite element analysis was developed and validated by experiment. Both experiment and simulation show that the MRP has a linear resonance frequency of 4.6 Hz and peak power of 3.7 mW. It exhibits strong nonlinear behaviours and broadband characteristics with excitation amplitude as low as 2 m/s2 in the primary resonance. As the excitation amplitude is larger than 5 m/s2 , the secondary resonance (1/2 order subharmonics) is excited. The responses of the MRP at the subharmonic resonance takes the same form as the primary resonance in terms of displacement and power outputs. This helps the subharmonic resonance to produce the same power level as the primary resonance but with a larger bandwidth. When excited at 14 m/s2 , the MRP shows 1-mW-bandwidth of 9.7 Hz, 2/3 of which is attributed to the subharmonic resonance.