Designing a phononic crystal with a defect for energy localization and harvesting: Supercell size and defect location

Abstract

Metamaterial-based energy harvesting (MBEH) has recently received much attention due to its capability of amplifying input mechanical wave transferred to a piezoelectric energy harvesting (PEH) device. A phononic crystal (PnC), one representative example of a metamaterial, is an artificially-engineered structure constituted by a periodic repetition of unit cells that can manipulate the propagation of elastic waves at the scale of the wavelength. If a defect is introduced in the PnC by replacing one unit cell with another cell that has different geometric or material properties, the periodicity of the PnC is locally broken; thereby, defect bands are created within the band gap. Since the defect can mechanically resonate with a certain defect mode shape at the defect band frequency, an evanescent wave can be localized inside the defect. By attaching the PEH device to the defect, the output electric power can be dramatically enhanced. However, there is presently no thorough design rationale to inform decisions on supercell size and optimal defect location of a PnC for energy localization and harvesting. Thus, this study investigates effects of supercell size and defect location on energy localization and harvesting performances. For a given defect location, the output performance of the PnC-based PEH system monotonically increases and converges toward the maximum value as the supercell size increases. For a given supercell size, there exists an optimal defect location where maximum output performances of the PnC-based PEH system can be achieved. The key findings of this study lie in that there is a trade-off relationship between the fulfillment of resonance formation and the attenuation of evanescent waves. It can be concluded from this study that the supercell size and defect location can be properly designed to improve the output performances of a PnC-based PEH system under elastic waves.