An analytical model of a piezoelectric-defect-introduced phononic crystal with partial debonding

Abstract

Piezoelectric energy harvesting (PEH) systems based on defect-introduced phononic crystals (PnCs) have exhibited enhanced power output; however, they are vulnerable to long-term degradation due to interfacial debonding. The present work proposes an initial analytical framework for a one-dimensional PnC embedding a defect that possesses bimorph PEH devices with symmetric partial debonding at its center. The analytical model under consideration features rigorous decomposition of wave-propagation behaviors across bonded/debonded, electroelastically coupled/decoupled regions. A transfer matrix with electroelastic coupling and partial debonding is newly derived, integrating Newton's laws, linear piezoelectric constitutive relations, and Gauss's law under harmonic excitation. Band-structure analysis via the transfer-matrix method quantifies defect-band frequency shifts and defect-mode shape changes induced by varying debonding ratios, while the S-parameter method predicts the variations of the frequency-response curves for the harvested current, voltage, and optimal electric power. The analytical predictions are validated against COMSOL Multiphysics, demonstrating excellent agreement over debonding ratios up to 80%. Notably, the results reveal a pronounced and nonlinear degradation of defect-band frequencies and PEH performance beyond an empirically identified debonding level of approximately 40%. The proposed analytical framework enables rapid and cost-effective assessment of debonding effects and provides useful insights into the design and material selection of more robust PEH devices.