Harmonic balance analysis of nonlinear tristable energy harvesters for performance enhancement

• The theoretical solutions and their stability of nonlinear tristable energy harvesters are presented based on the harmonic balance method and the Jacobian matrix.
• The sensitivity of dynamic characteristics to the system parameters values of nonlinear tristable energy harvesters is investigated.
• The promising potential for performance enhancements is numerically demonstrated using high-energy orbits in the multi-solution range.
• Experimental results verify the multi-solution range corresponding to the excitation frequency and amplitude in theoretical analysis.

Nonlinear energy harvesters are very sensitive to ambient vibrations. If the excitation level is too low, their large-amplitude oscillations for high-energy voltage output cannot be obtained. A nonlinear tristable energy harvester has been previously proposed to achieve more effective broadband energy harvesting for low-level excitations. However, the sensitivity of its dynamic characteristics to the system parameters remains uninvestigated. Therefore, this paper theoretically analyzes the influence of the external load, the external excitation, the internal system parameters and the equilibrium positions on the dynamic responses of nonlinear tristable energy harvesters by using the harmonic balance method. In addition, numerical acceleration excitation thresholds and basins of attraction are provided to investigate the potential for energy harvesting performance enhancement using the suitable equilibrium positions, appropriate initial conditions or external disturbances, due to high-energy interwell oscillations in the multi-solution ranges. More importantly, experimental voltage responses of a given tristable energy harvester versus the external excitation frequency and amplitude verify the existence of experimental multi-solution ranges and the effectiveness of the theoretical analysis. It is also revealed that achieving high-energy interwell oscillations in the multi-solution ranges of tristable energy harvesters will be feasible for improving energy harvesting from low-level ambient excitations.