Dynamics and power limit analysis of a galloping piezoelectric energy harvester under forced excitation

This paper presents a rigorous analytical solution to the dynamics of a single-degree-of-freedom (SDOF) piezoelectric energy harvester (PEH) under the combined wind and base excitations using the harmonic balance method. The boundaries of the quenching region are predicted using the multi-scale method. An equivalent circuit model (ECM) is established to verify the analytical solution, and the simulation results based on the ECM are in good agreement with the analytical ones. Subsequently, the power limit of the SDOF PEH under the combined excitations is analysed for the first time using the impedance theory based on a simplified model. The maximum power amplitudes at different excitation frequencies are also sought by numerically sweeping the load resistance. It is found that the impedance theory that has been successfully adopted in the literature is inapplicable in analysing the power limit of the SDOF PEH under the combined excitations. The impedance plots obtained based on resistance sweeping clearly indicate that, in contrast to the conclusions given in the literature, impedance matching is not the condition to attain the power limit of the SDOF PEH under the combined excitations. A mathematical proof is provided for a reasonable explanation. Finally, it is demonstrated that numerical simulations based on the original model can verify the power limit calculated based on the simplified model.