Nonlinear dynamics of a double-pendulum energy harvester under low-frequency excitation: Theoretical modeling and numerical study

Wearable devices are increasingly used in our daily life, but still face challenges in sustainable power supply. Energy harvesting technology provides a feasible solution. To achieve effective harvesting of low-frequency random kinetic energy from the human body, this study investigates a double-pendulum energy harvester with electromagnetic transduction. The harvester comprises two serially connected pendulums, with magnets attached on the secondary pendulum enabling electromechanical energy conversion. A nonlinear dynamic model has been established to characterize the system’s behavior, revealing three distinct motion modes: chaotic states, periodic oscillations, and rotational movements. Bifurcation analysis uncovers complex transitions between these modes, while frequency spectral analysis illustrates that the emergence of new frequency components significantly enhances energy output. Parametric studies show that increasing the primary pendulum’s mass shifts the system toward single-pendulum behavior, whereas elongating the primary pendulum reduces the critical excitation frequency for chaos onset. Its highest average power reaches 1.45 mW when the excitation frequency is 2.96 Hz under a fixed amplitude of 0.1 m. The inherent nonlinearity of the double-pendulum configuration enables rich dynamic responses under low-frequency excitation while maintaining stable power output across broad parameter ranges (0.1 ∼ 0.3 m, 1.8 ∼ 3 Hz). Experimental result shows that under human running excitation, the device can achieve an average output power of 1.3 mW. These findings underscore this concept’s potential for reliable energy harvesting in wearable applications.