A modified magnetic force model and experimental validation of a tri-stable piezoelectric energy harvester

Nonlinear tri-stable piezoelectric energy harvesters with magnetic field coupling have attracted many researchers' interest in ambient vibration energy harvesting and conversion. In such a tri-stable piezoelectric energy harvester, the nonlinear magnetic force generated by the external magnetic field is mainly calculated by the equivalent magnetic dipole method. However, this method will give highly erroneous results when the magnetic separation distance is small. This study presents a modified magnetic force model to precisely calculate the nonlinear magnetic force exerted on the tip of the cantilever beam. Unlike the equivalent magnetic dipole method regarding the magnet as a point dipole at its body center, this model only considers the surface magnetization current of the left and right surfaces of the magnets and replaced them by the one of the center point dipoles on these associated surfaces. With this model, the nonlinear magnetic force, the potential energy, and the transition mechanism of the tri-stable piezoelectric energy harvester are numerically investigated. Experimental validations are consequently performed to testify the numerical results. Compared with the equivalent magnetic dipole method, the modified magnetic force model has a much higher accuracy to be more applicable for different magnetic separation distances, especially when the magnetic separation distance is small.