Dynamic and energetic characteristics of a tri-stable magnetopiezoelastic energy harvester

• We propose and model a tri-stable magnetic repulsion piezoelectric energy harvester.
• Bifurcation analysis is performed to explore the multi-stability formation mechanism.
• Bifurcation set diagram, a useful stability map to design the harvester, is obtained.
• Nonlinear dynamic and energetic performances of the energy harvester are examined.

In this study, a mathematical model of a tri-stable energy harvester is developed and used to investigate its formation mechanisms for multi-stability states, nonlinear dynamic behaviors, and power generation performance. Bifurcation analyses for the equilibrium solution of the derived model system are performed. It is shown that the present energy harvester system can exhibit multi-stable (mono-, bi-, and tri-stable) behaviors depending on the two geometric parameters associated with the locations of the tip and external magnets. It is also found that the tri-stability is initiated by a new pitchfork bifurcation or a degenerate pitchfork bifurcation that leads to a pair of saddle-node bifurcations. Bifurcation set diagram is obtained in the parametric space of these two geometric parameters, which can be used to design the potential wells of the multi-stable energy harvesters. Potential energy diagrams are also obtained and they show that the distance between the outer potential energy wells for the tri-stable state is formed in a way that it is larger than that for the equivalent bi-stable state. A series of numerical simulations performed on the present system well illustrates the high output power generation characteristics of the tri-stable energy harvester over a broad operating frequency band.