A numerical dynamic analysis of a bistable magnetic rolling pendulum for multi-directional vibrational energy harvesting

Abstract Magnetic rolling pendulum (MRP) is extensively utilized for harvesting vibrational energy, owing to its advantage of significantly reduced mechanical dissipation. Nevertheless, the MRP harvester’s nonlinear dynamics when subjected to a multi-directional vibrational environment remains an open issue. This paper conducts a numerical study to explore the intricate dynamic responses of a bistable magnetic rolling pendulum (BMRP) subjected to multi-directional excitation for energy harvesting. Numerical simulations under sweep frequency excitation, grounded in both theoretical modeling and finite element analysis, reveal that an optimal direction exists for the BMRP, enabling large-amplitude interwell oscillations in period-1 at lower frequencies and in period-2 at higher frequencies. Under multi-directional constant frequency excitation, the bifurcation and multi-solution phenomena of the systems with different potential well depths are examined. Numerical results illustrate that the number of possible solutions under certain conditions and the probability of each solution occurring are intimately tied to the frequency, amplitude, direction of the excitation, and the potential well depth. Generally speaking, this study introduces an innovative approach for scavenging energy from the multi-directional vibrational environment, opening up new possibilities for advancements in energy harvesting technology.