Enhancement of the performance of a hybrid nonlinear vibration energy harvester based on piezoelectric and electromagnetic transductions

A multiphysics model of a hybrid piezoelectric-electromagnetic vibration energy harvester (VEH), including the main sources of nonlinearities, is developed. The continuum problem is derived on the basis of the extended Hamilton principle, and the modal Galerkin decomposition method is used in order to obtain a reduced-order model consisting of a nonlinear Duffing equation of motion coupled with two transduction equations. The resulting system is solved analytically using the method of multiple time scales and numerically by means of the harmonic balance method coupled with the asymptotic numerical continuation technique. Closed-form expressions for the moving magnet critical amplitude and the critical load resistance are provided in order to allow evaluation of the linear dynamic range of the proposed device. Several numerical simulations have been performed to highlight the performance of the hybrid VEH. In particular, the power density and the frequency bandwidth can be boosted, by up to 60% and 29% respectively, compared to those for a VEH with pure magnetic levitation thanks to the nonlinear elastic guidance. Moreover, the hybrid transduction permits enhancement of the power density by up to 84%.