Harmonic analysis and experimental validation of bistable vibration energy harvesters interfaced with rectifying electrical circuits

The high-performing, nonlinear vibration energy harvesters are conventionally investigated when integrated with simplified resistive electrical circuits (AC circuits), while in fact DC voltages are needed for electronics and rechargeable batteries in practical applications. To lead to an accurate and effective set of design guidelines for realistic energy harvesting system development, an analytical, harmonic balance based method is proposed to characterize the steady state performance and investigate the DC circuit effects. During the route of the analysis method, the induced nonlinear, piecewise piezovoltage is firstly approximated via smooth dynamic responses based on the energy equivalence, which enables the followed harmonic balance operation to analytically estimate the vibration amplitude. The parameter studies show the pros and cons of the coupling constant and resistive load. In one side, with increasing the coupling constant or load resistance during their moderate range, higher electric power is extracted. In the other side, higher piezoelectric coupling and resistive load compromise the beneficial bandwidth of snap-through vibrations. Moreover, comparisons are conducted to reveal the different structural roles of the standard electrical circuit and AC circuit. It is found that AC circuit exhibits equivalent damping effect while the standard rectifying electrical circuit exhibits both equivalent damping and stiffness effects to the harvester system. These different circuit effects explain the theoretically predicted and numerically validated phenomena that the standard rectifying electrical circuit extracts less electric power than AC circuit under moderate piezoelectric coupling constants and resistive loads, while outperforms AC circuit when the coupling constants or load resistances are relatively large.