Zero-phase propagation in realistic plate-type acoustic metamaterials

Abstract

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Experimental evidence of a hiding zone in a density-near-zero acoustic metamaterial

“…A large impedance mismatch at the zero-phase propagation frequency prevents total transmission, the magnitude of which is moreover strongly dependent on the number of unit cells, i.e., number of plates, in the system. 39 Losses, mainly due to the viscoelasticity of the plate and characterized by the loss factor β, strongly alter the amplitude of the transmission at the zero-phase frequency, which drops from jT f¼0 j ¼ 0:91 in the lossless case to jT f¼0 j ¼ 0:48. The zero-phase frequency is shifted to f f¼0 ¼ 389 Hz, while the maximum of transmission jT m j ¼ 0:61 is found at f m ¼ 439 Hz, which is the resonance frequency of the lossy plate as reported in Ref.…”

“…[36][37][38] In this latter case, strong dispersion around the resonance frequency allows to achieve zerodensity, unitary transmission, and zero-phase at three distinct frequencies in the vicinity of the bandgap edge. 39 Gu et al state that cloaking is achievable in a membrane-type metamaterial and report a numerically obtained enhanced transmission through obstacles embedded in a two-dimensional square arrangement of lossless membranes. 40 Nevertheless, a trade-off has to be made between the transmission magnitude and the phase shift induced by the membranes array.…”

Doping of a plate-type acoustic metamaterial

“…The acoustic constitutive parameters analogous to ε and µ are respectively the density ρ and the compressibility C (inverse of the bulk modulus κ). Quasistatic field distribution and zero-phase propagation can therefore be achieved using Compressibility and Density-Near-Zero (DCNZ) [36,37], Compressibility-Near-Zero (CNZ) [26] or Density-Near-Zero (DNZ) media [27][28][29][30][31]. A periodic arrangement of thin elastic plates (or membranes) in air -a Plate-type Acoustic Metamaterial (PAM) -makes the DNZ condition possible thanks to the strong dispersion around the band gap associated with the plate resonance.…”

“…A periodic arrangement of thin elastic plates (or membranes) in air -a Plate-type Acoustic Metamaterial (PAM) -makes the DNZ condition possible thanks to the strong dispersion around the band gap associated with the plate resonance. Such a system can be characterized with the help of three different frequencies [31]. The impedance matching occurs at the plate resonance frequency but is accompanied by a phase delay depending on the length of the system.…”

“…We consider a 1D periodic arrangement of N = 20 thin clamped elastic shims (plastic with a Young's modulus E = 4.6 GPa, density ρ = 1400 kg.m −3 , Poisson's ratio ν = 0.41, thickness h = 102 μm) equally spaced by a distance L gap = 1 cm and plugged into a waveguide of radius R a = 15 mm. The properties of such a PAM have been extensively studied [29][30][31].…”