Homogenization and analysis of planar piezoelectric metamaterials: A comprehensive study

Abstract

This article presents a comprehensive investigation into the homogenization and analysis of planar piezoelectric metamaterials. The classical transfer matrix method is extended by using homogenization methods to evaluate the sound transmission of piezoelectric metamaterials in both normal and oblique incidences. This has been validated numerically using the finite element method and experimentally in the solid medium propagation in normal incidence. Several vibro-acoustic analytical models are compared in oblique incidence, including the Kirchhoff thin plate theory, the Reissner-Mindlin thick plate theory, and the theory of wave propagation in elastic solids. These theories are used to determine the dispersion relation, coincidence, and transition frequency of thin and thick plate theories in analyzing piezoelectric metamaterials. Additionally, acoustic properties of piezoelectric layers connected to external circuits are parametrically studied, exploring both dimensional and dimensionless variables. Results indicate that significant control over the resonance frequency and sound transmission can be enabled by adjusting the external electrical impedance, flat-layer structures, and piezoelectric materials. This demonstrates excellent tunability and compactness of planar piezoelectric metamaterials for space-sensitive applications. The study indicates a straightforward and powerful analytical approach for the optimization of acoustic insulation using planar piezoelectric metamaterials.