Spherical Inclusions Based Defect Modes in a Phononic Crystal for Piezoelectric Energy Harvesting

Abstract

AbstractThis paper proposes a Phononic crystal (PnC) device formed by embedding spheres in a polymer matrix for energy harvesting, an application that has drawn much research interest recently. A parametric study is performed to evaluate the optimal radius to lattice parameter ratio r/a = 0.4 to obtain a large bandgap as well as gap to mid-gap ratio. By removing a sphere from the central lattice point, a defect is created within an otherwise perfect PnC. The supercell technique is employed to compute defect modes and band structure of defect PnC. These defect bands show strong vibrational modes within the spatial arrangement of the defect point and these defect frequencies appear to be flat (dω/dk = 0) in the band structure confirming energy localization at these modes. Also, while varying the radius of the defect sphere rd in the range of [0.1a–0.5a], the number of defect modes within the bandgap tend to decrease, vanishing when rd equals 0.4a and 0.5a. To utilize the defect mode for energy harvesting, a small patch made of a piezoelectric material is attached onto the PnC device exactly above the defect. Introduction of this patch renders the band structure and defect modes to shift upwards compared to the defect PnC without the patch. A highly localized vibrational eigen mode is observed around 662 kHz in the band structure for the defect PnC with patch. The voltage response of this device is simulated by connecting a high resistance (open-circuit) to the patch and sweeping frequencies around the defect mode. This process produced a voltage of 2.8 V at 656.7 kHz for a 0.3 µm displacement excitation, thus demonstrating the usefulness of the proposed concept.KeywordsPhononic crystalSpherical inclusionDefect modesMetamaterialPiezoelectric energy harvesting