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This study systemically investigates a porous labyrinthine type of acoustic metamaterials (LAMs), a sort of acoustic metasurface, analytically, numerically, and in laboratory tests. The LAMs are composed of a series of porous elements, where stainless steel plates with various lengths are inserted into the melamine foam. At the frequency of interest 2000 Hz, porous elements with a thickness smaller than one-eighth of the target wavelength are designed to generate a linearly varied phase gradient on the refracting surface and slightly varied phase responses on the reflecting surface; the elements play key roles in refracted and reflected wave manipulations, respectively. Two porous LAMs with different periodical lengths are designed based on the generalized Snell's law to study the effect of the periodical length on refraction and reflection phenomena in the scattered sound pressure fields. By reducing the length to smaller than one-half of the target wavelength, the high-order wave modes will disappear in the refracted and reflected sound pressure fields at omnidirectional incidence, resulting in enhancements of transmission loss and also sound absorption coefficient in a wide range of incidence angles compared with the uniform melamine foam with the same thickness. The thin porous LAMs provide a method to improve sound transmission loss and sound absorption properties of an uniform porous material and show potentials to be used in cabins of high-speed trains and aircraft. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In rods and beams, piezoelectric patches with external circuits have been extensively studied to dampen structural vibrations at the sound source. This work uses a large flat-layer type of piezoelectric acoustic metamaterial (AM) model for noise attenuation in the sound transmission stage rather than at the sound source. This could be directly implemented as a large space sound transmission barrier at the interface of diverse media including gas, liquid, and solid materials. The general analytical model to derive acoustic properties of the piezoelectric acoustic metamaterial is established by the equivalent transfer matrix approach for normal incidence waves. This has been validated numerically using the finite element method and experimentally in the solid medium propagation for the first time. Moreover, a parametric study of sound transmission properties in air, water, and steel is conducted by adjusting external circuit parameters, flat-layer structures, and piezoelectric materials. The findings demonstrate the ability to control sound resonance frequency and bandwidth through the propagation process over a wide range using external circuit parameters alone. This endows the piezoelectric acoustic metamaterial with great versatility relative to conventional, fixed structure, metamaterials used as sound barriers at the interface of diverse media. In addition, the size of the piezoelectric AM can reach a deeply sub-wavelength level, less than 1 0 − 3 of the resonance wavelength in both water and solid media, which goes far beyond the wavelength-to-thickness ratio of classical acoustic metamaterials. The layer-type piezoelectric AM thus shows excellent performance in tunability and compactness for space-sensitive applications as well as great potential in combining metamaterials with electronic control. [Display omitted] • Develop a large flat-plate piezoelectric AM model to attenuate sound transmission. • Applicable to diverse media interfaces including gas, liquid, and solid materials. • Experimentally validated in the sound transmission stage for the first time. • Adjust resonance frequency and bandwidth over a wide range by external circuits. • Deeply sub-wavelength structure size: less than 1/1000 of the resonance wavelength. [ABSTRACT FROM AUTHOR]