Nonlinear double-mass pendulum for vibration-based energy harvesting

To enhance the performance of a vibration-based energy harvester, typical approaches employ frequency-matching strategies by either using nonlinear broadband or frequency-tunable harvesters. This study systematically analyzes the nonlinear dynamics and energy harvesting performance of a recently emerging tunable low-frequency vibration-based energy harvester, namely, a double-mass pendulum (DMP) energy harvester. This energy harvester can, to some extent, eliminate frequency dependence on pendulum length but exhibit vibration-amplitude-dependent softening nonlinearity. The natural frequency of the DMP structure is theoretically derived, showing several unique characteristics compared with the typical simple pendulum. The DMP energy harvester exhibits alternate single-period, multiple-period, and chaotic vibration behaviors with increase in excitation amplitudes. The analysis of gross output power indicates that the rotating motion, regardless of chaotic or periodic rolling motions, improves the energy harvesting performance in terms of power leap and broader bandwidth. Based on the parameter space analysis, the rotating motions usually occur at the shift-left locations of frequency ratios 1 and 2; a smaller damping ratio corresponds to a lower on-demand excitation amplitude for the rotating-motion occurrence. Numerical results confirm that the DMP is suitable for low-frequency energy harvesting scenarios, suggesting the realization of rotating motion for improving energy harvesting performance. Moreover, a shake table test was performed, and the experimental results validated the accuracy and effectiveness of the DMP modeling analysis. Practical issues related to DMP energy harvesters under different types of excitations are finally discussed. Although the analysis is for the DMP, the corresponding conclusions may shed light on other pendulum-type energy harvesters.