Bifurcation and multi-solution phenomena of a parametrically excited magnetic rolling pendulum bistable energy harvester

Previously, the mechanism of the magnetic rolling pendulum (MRP) has been employed in energy harvesting, attributed to its minimal mechanical loss. However, there has been a lack of studies concentrating on the exploration of MRP harvesters that exhibit bistable characteristics resulting from an external adjustable magnet. Consequently, this paper delves into the bifurcation and multi-solution phenomena of MRP bistable energy harvesters (MRP-BEHs) under parametric excitation. By utilizing the finite element analysis in conjunction with the established dynamic model, the electrical output is predicted. Under conditions of sweep frequency excitations, the broadband response characteristic of the MRP-BEH is verified numerically and experimentally, and experimental results demonstrate the occurrence of large-amplitude interwell oscillations within the frequency range spanning from 5.2 to 21.25 Hz when the excitation level is set at 0.45 g. Utilizing the dynamic model validated through experiments, the bifurcation analysis is undertaken by considering systems with different potential energy functions. Results reveal that the system exhibits complex dynamic behaviors and shallower potential wells facilitate low-frequency operation. Additionally, an investigation into the multi-solution phenomena of the MRP-BEH under parametric excitation is conducted via basins of attraction. Numerical findings demonstrate a strong correlation between the number and vibrational pattern of solutions and factors such as excitation amplitude, frequency, and potential energy functions. Overall, this comprehensive experimental and numerical investigation provides new insights into the parametrically excited MRP-BEHs, a wide and still less explored topic.