Phononic band gap of a quarter-wave stack for enhanced piezoelectric energy harvesting

Extraordinary phenomenon (e.g., band gap) exhibited by a phononic crystal (PnC) has recently been incorporated into piezoelectric energy harvesting (PEH) as a means to amplify input waves for improving the power generation capability. For a systematic design of PnC-based PEH using band gap reflection, it is required to identify a standing wave pattern (i.e. location of nodes and antinodes) in order to determine the optimal placement of a piezoelectric layer. In this context, we propose a quarter-wave stack (QWS)-based PEH system under elastic waves. The foundational idea of this study is to manipulate a standing wave pattern formed in a host medium by considering the phase change within the QWS. The key to creating an optimal standing wave for PEH is to intentionally form a displacement node at the interface between the host medium (here, continuous copper bar) and QWS at a target design frequency; thereby, the placement of the piezoelectric layer can be systematically determined in order that its center is aligned with the strain antinode to generate the maximum output power. To deeply explore the effect of the standing wave pattern on the output performances of the QWS-based PEH system, two key parameters are thoroughly investigated: 1) the number of unit cells and 2) the excitation frequency. Numerical analysis results suggest the followings: First, an increase in the number of unit cells corresponds to the effect of amplifying input loading for enhanced PEH; thereby, the output performances increase gradually and converge asymptotically. Second, since the standing wave pattern varies with the excitation frequency, the electroelastic coupling varies accordingly. These new findings provide guidelines on design parameters that can be manipulated to yield the best performance of the QWS-based PEH system under elastic waves for various potential applications.