Investigation of snap-through and homoclinic bifurcation of a magnet-induced buckled energy harvester by the Melnikov method

Snap-through is used to improve the efficiencies of energy harvesters and extend their effective frequency bandwidths. This work uses the Melnikov method to explore the underlying snap-through mechanism and the conditions necessary for homoclinic bifurcations in a magnet-induced buckled energy harvester. First, an electromechanical model of the energy harvester is established analytically using the Euler-Bernoulli beam theory and the extended Hamilton's principle. Second, the Melnikov function of the model is derived, and the necessary conditions for homoclinic bifurcations and chaos are presented on the basis of this model. The analysis reveals that the distance between the magnets and the end-block mass significantly affect the thresholds for chaotic motions and the high-energy solutions. Numerical and experimental studies confirm these analytical predictions and provide guidelines for optimum design of the magnet-induced buckled energy harvester.