Mechanically and electrically nonlinear non-ideal piezoelectric energy harvesting framework with experimental validations

In the literature of vibration energy harvesting, mechanically nonlinear frameworks have mostly employed linear electrical circuitry to formulate AC input–AC output problems, while the existing efforts on nonlinear power conditioning circuits have assumed linear mechanical behavior. However, even for the simplest case of a stiff (geometrically linear) piezoelectric cantilever, material softening and dissipative nonlinearities in the mechanical domain have to be accomodated to accurately predict the response for moderate to high excitation levels, and likewise a stable DC signal must be obtained to charge a storage component in realistic energy harvesting applications. Furthermore, often times the voltage output is not large enough to assume ideal diode behavior to reduce diodes to switches in AC–DC conversion modeling. Therefore, a relatively complete representation of piezoelectric energy harvesting requires accounting for the mechanical (e.g., material and dissipative) nonlinearities as well as the nonlinear process of AC–DC conversion with non-ideal circuit elements, such as real diodes. To this end, we present and experimentally validate a multiphysics framework and harmonic balance analysis that combines these mechanical and electrical nonlinear non-ideal effects to predict the DC electrical output (DC voltage across the load) in terms of the AC mechanical input (base vibration) for arbitrary vibration and voltage levels. The focus is placed on a bimorph cantilever with piezoelectric laminates under base excitation. The terminals of the piezoelectric layers are combined in series and connected to a bridge rectifier with non-ideal diodes and a filter capacitor. The multi-term harmonic balance framework can capture the ripple in the DC signal as well as amplitude-dependent nonlinear dynamics accounting for realistic diode behavior. In addition to quantitative comparisons and validations by comparing the experimental data and model simulations, important qualitative trends are unveiled for mechanically and electrically nonlinear non-ideal dynamics of piezoelectric energy harvesting.