Nonlinear modeling and study of rigid-flexible piezoelectric energy harvester with additional frame

Abstract

Based on a rigid-flexible piezoelectric energy harvester (PEH) composed of antisymmetric double plates with a rigid frame, which has three operating bandwidths in a low-frequency range, nonlinearity is used to further broaden the operating bandwidth. Firstly, finite-element simulation is used to study the influence of structural parameters, such as the width of the frame and the distance between two plates, on the natural frequencies. Bending deformation of cantilever plates and rigid motion of frame are considered comprehensively to obtain the theoretical mode functions of the structure. The nonlinear electromechanical coupling model is established via von Karman nonlinear geometric assumptions and the Hamilton principle. In order to study the broadening of output bandwidth caused by nonlinearity, the average equations with 1:1.5:2 internal resonance ratio are derived by the multi-scale method. On the basis of the calculated optimal resistance, the voltage response and dimensionless amplitude response curves induced by the first three order modes are numerically calculated. Theoretical analysis shows that the proposed PEH not only obtains three peaks of voltage output in a low-frequency range, but also utilizes hard spring effect and internal resonance to widen the output bandwidth of each resonance interval.