Nonlinear magnetic force and dynamic characteristics of a tri-stable piezoelectric energy harvester

In piezoelectric energy harvesters (PEHs) with external magnetic coupling, one main challenge is to obtain a precise magnetic force model to calculate the impacts of the external magnetic force on the vibrational response and energy harvesting performance. A tri-stable piezoelectric energy harvester (TPEH) with two external magnets was considered in this paper. An improved magnetic force model based on the magnetic dipoles theory was originally derived to investigate the formation mechanisms for bi- or tri-stability states at first, and then, a distributed-parameter mathematical model based on the energy method was established by considering the derived nonlinear magnetic force, and was used to investigate the nonlinear dynamic behaviors and power generation performance. Bifurcation analyses were also performed for the equilibrium solution of the derived system model. Experiments were subsequently conducted to validate the theoretical analysis. Simulation and experimental results indicate that the improved model for magnetic force is more applicable compared with the magnetic dipoles model used before. Results also show that the TPEH can significantly enhance the energy harvesting performance compared with the conventional bi-stable piezoelectric energy harvester in a wide frequency range.