Mathematical Model Development, Experimental Validation and Design Parameter Study of A Folded Two-Degree-of-Freedom Piezoelectric Vibration Energy Harvester

A folded two-degree-of-freedom piezoelectric vibration energy harvester has been proposed by several researchers including the authors. It is characterized by the reversal of the modal sequence, which enhances the electrical output power near a target operating frequency with very little eigenfrequency separation. However, no appropriate mathematical models have yet been developed, though a well-developed one would clarify the physical behaviors and allow efficient investigations of the effects of design parameters. In this work, a rigorous mathematical model based on the continuous Euler–Bernoulli beam theory is proposed for the first time. It is validated by both a finite element analysis and by experimental measurements. The validated mathematical model is then employed for a design parameter study with four design parameters, in this case the length of each component beam and the magnitude of each proof mass. For certain selected cases from the design parameter study sets, prototypes are fabricated and their performances are measured for verification of the design parameter study. Some useful observations are also drawn from the design parameter study for the design of a high-performance folded two-degree-of-freedom piezoelectric vibration energy harvester. Through all of the results presented in this work, it is shown that the proposed mathematical model will serve as an effective tool for the analysis and design of a folded two-degree-of-freedom piezoelectric vibration energy harvester.