Global dynamic analysis of a typical tristable piezoelectric energy harvester for performance enhancement

Tristable piezoelectric energy harvesters (TPEHs) have been widely studied in recent years. Previous works have illustrated the persistent coexistence of high-energy and low-energy responses. Jumps among the responses can be induced by unavoidable initial-condition disturbances of TPEHs in practice, which concerns the final output of the harvested energy. For a more accurate evaluation of the TPEH performance, the disturbances of initial conditions should be taken into account. This study focuses on global dynamics of a typical TPEH with two fixed external magnets. Via static bifurcation analysis of the TPEH oscillatory system, the separation and gap distances are identified as key parameters to configure triple potential wells. The primary resonance analysis of the intra-well and inter-well responses is carried out to determine the optimum separation distance for efficient energy harvesting. Then, sequences of attractors and their basins of attraction (BAs) with the rise in the ambient excitation level and frequency is illustrated, showing that initial conditions of the TPEH system perturbed within the central well are beneficial for energy harvesting. For a low-level base excitation, BAs outside of the triple wells are severely fractal where the perturbation of the initial state of the TPEH can easily induce a jump that implies the unreliability of the TPEH performance. At a much higher ambient excitation level, the high-energy inter-well response can be globally attractive and reliable, which is preferable for practical applications of energy harvesters.