Applicability of magnetic force models for multi-stable energy harvesters

Multi-stable piezoelectric energy harvesters have been exploited to enhance performance for extracting ambient vibrational energy from a broadband energy source. Since magnetic force plays a significant role in enhancing the dynamic behavior of harvesters, it is necessary to model and understand the significant influencing of structural parameters on magnetic force. Recently, several theoretical modeling methods, including magnetic dipole, improved dipole, magnetic current, and magnetic charge models, have been developed to calculate the magnetic force in multi-stable energy harvesters. However, the influence of structural parameters and magnet dimensions on the accuracy of magnetic force calculation for these methods has not been analyzed. Therefore, it is necessary to investigate the applicability of these methods under a range of operating conditions. New insights into the accuracy and application constraints of these methods are presented in this paper to calculate the impact of magnetic force on multi-stable energy harvesters. From the theoretical derivation of models and numerical results obtained, a quantitative assessment of errors under different structural parameters and magnet sizes is presented and compared to evaluate the application constraints. Moreover, experimental measurements are performed to verify the applicability of these modeling methods for bi-stable and tri-stable energy harvesters with different structural parameters.