Dynamics characterization of a class of custom slide model piezoelectric energy harvester

This paper examines the overall dynamic behavior of a customized sliding track used in conjunction with a piezoelectric cantilever beam energy harvester. The sliding track is designed to slide over a spring, inducing oscillations in the cantilever beam. Three different types of sliding orbits, namely monostable, bistable, and tristable, are tailored for investigating the performance of the energy harvester. Initially, we develop a mathematical model to describe the system dynamics and discuss the equilibrium steady state and potential well of its dimensionless form. To analyze periodic solutions near the equilibrium points for all three models, we employ a multiscale method that addresses saddle-knot bifurcation problems. To validate our predictions, we utilize numerical simulations based on the 4th Runge-Kutta method along with point mapping techniques to determine coexisting attractors and their domains of attraction. The results obtained from these simulations align closely with our theoretical predictions, demonstrating that at low frequencies, the three-steady-state model exhibits superior energy harvesting performance. This research has significant implications for optimizing piezoelectric energy harvesters through structural design.