Optimized Nonlinear MDOF Vibration Energy Harvester Based on Electromagnetic Coupling

Vibration energy harvesters (VEHs) provide an efficient solution for implementing self-sustained low power microelectromechanical systems. When operating linearly, unimodal VEHs have a narrow operating bandwidth. Consequently, their performances can be significantly reduced if the VEH resonance frequency and the excitation frequency do not coincide. In order to overcome this issue, we propose an optimized nonlinear multi-degree of freedom (MDOF) vibration energy harvesting system based on electromagnetically coupled beams. The dynamic equations of the equivalent discrete nonlinear MDOF model, which include the magnetic nonlinearity, the mechanical nonlinearity due to the mid-plane stretching of the beams and the electromagnetic damping, are derived and numerically solved using the harmonic balance method coupled with the asymptotic numerical method. A multiobjective optimization procedure is defined and performed using a non-dominated sorting algorithm (NSGA) in order to find the optimal solution in terms of performances by taking advantage of the nonlinear coupling and the modal interactions. The proposed strategy enables scavenging the vibration energy with a frequency bandwidth ranging from 22 to 32 Hz and a normalized harvested power of 312 µW cm⁻³ g⁻².