Planar piezoelectric metamaterials: Sound transmission and applicable frequency range in oblique incidence

Frequency limit and applicable frequency range of planar piezoelectric metamaterials connected to external circuits have not been well defined in estimating the sound transmission loss. This article extends the classical transfer matrix method for use in evaluating the sound transmission of thin-plate piezoelectric metamaterials in oblique incidence. Using the Kirchhoff thin plate theory, a modified transfer matrix method that takes factors of external circuits into consideration is developed for attenuation and control of acoustic waves. Several vibro-acoustic analytical models are compared, 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 analysing piezoelectric acoustic metamaterials, alongside a validation using the finite element method. Then acoustic properties of piezoelectric plates connected to passive external circuits are studied parametrically with both dimensional and dimensionless variables based on an equivalent Kirchhoff plate approximation. The findings show that external electrical impedance alone can be used to adjust the resonance frequency over a broad range and thereby control sound transmission loss. This provides considerable flexibility in modifying the acoustic properties of the piezoelectric metamaterial in comparison to traditional, fixed-structure metamaterials. The study indicates a straightforward and powerful analytical approach for the optimization of acoustic insulation using thin-plate piezoelectric metamaterials. •Derive freq limit of planar piezo metamaterial and explore applicable frequency range.•Simplify by removing periodic patches bonded on a plate, cutting complexity and cost.•Introduce dimensional analysis to reduce variables and improve insight through analogy.•Emphasize considering multiple plate models in planar piezo metamaterial design.•Spot applications to reduce noise at varied frequencies in rotor operation.