Homoclinic bifurcation threshold of a bistable system for piezoelectric energy harvesting

In this work, we study the homoclinic bifurcation threshold of a bistable energy harvesting system, which can be used to determine the presence of the high energy orbit and improve the harvesting efficiency. The equivalent mathematical model of piezoelectric beam compressed by axial force is proposed, which becomes a bistable energy harvester as axial load goes beyond the critical load. Based on Melnikov theory, a global method is presented to qualitatively analyze the motion of the system when it is excited by harmonic base motion. From the global method, the criteria of homoclinic bifurcation are derived. The analysis results are verified via bifurcation diagram and Lyapunov exponent. Numerical simulations show that cross-well oscillation occurs as critical threshold condition is satisfied, which makes the power ratio between output and input reach the maximum. The agreements between the analytical results and those from numerical simulation validate the effectiveness of the proposed technique.