Accurate modeling, comparative analysis, and performance enhancement of broadband piezoelectric energy harvesters with single and dual magnetic forces

The accurate electromechanical modeling and effectiveness of a piezoelectric energy harvester having dual magnetic forces at its tip is evaluated for low-frequency excitation purposes. To accurately represent the magnetic force, the exact finite element magnetic force is accurately fitted with a fifth-order polynomial representation in order to use it for low spacing distances between the two magnets. A comparative study is then carried out between the performances of piezoelectric energy harvesters having single and dual magnetic forces. It is indicated that hardening nonlinear behaviors take place in the dual attractive magnets compared to softening behaviors in the single magnet design. Static and eigenvalue problem analyses are also performed in order to determine the impacts of the spacing distance between the magnets on the static deflection and fundamental natural frequency of the energy harvester. The results show that the inclusion of a second magnetic force with an attractive interaction results in a delay in the static pull-in and a decrease in the fundamental natural frequency for same spacing distances. After that, a nonlinear distributed-parameter model is derived using the Galerkin discretization and used to study the performance and effectiveness of a piezoelectric energy harvester with dual attractive magnetic forces. The results show that the attractive dual magnets with same spacing distances lead to the presence of broadband resonance regions when the spacing distance between the magnets decreases to lower values. In addition, unlike the dual magnetic forces configuration which has only cubic nonlinearity, it is demonstrated that the single magnetic force configuration results in the presence of the quadratic nonlinearity which allows the energy harvester to have a softening behavior.