Homoclinic bifurcation for a bi-stable piezoelectric energy harvester subjected to galloping and base excitations

Abstract

In this paper, we studied the homoclinic bifurcation and nonlinear characteristics of a bistable piezoelectric energy harvester while it is concurrently excited by galloping and base excitation. Firstly, the electromechanical model of the energy harvester is established analytically by the energy approach, the Kirchhoff's law and quasi-steady hypothesis. Then, by the Melnikov method, the threshold for underlying snap-through in the system is derived, and the necessary conditions for homoclinic bifurcation and chaos are presented. The threshold is a determinant for the occurrence of high-energy oscillation. The analysis results reveal that the wind speed and the distance between magnets could affect the threshold for inter-well chaos and high energy oscillation. Finally, numerical simulation and experiments are carried out. Both results from numerical simulation and experiment support the theoretical prediction from Melnikov theory. The study could provide a guideline for the optimum design of the bi-stable piezoelectric energy harvester for wind and vibration in practice.