Sound absorption by viscoelastic coatings with periodically distributed cavities

Abstract

Thin rubber layers with air-filled cavities can be used as anechoic submarine coatings. Normally incident sonar energy is redistributed in the lateral direction and absorbed. In this paper, the anechoic effect is studied theoretically and numerically by adapting techniques used in electron scattering and band-gap computations for photonic and phononic crystals. Reflection and transmission matrices are computed recursively, from basic ones for layers containing periodic arrays of spherical cavities. A method to locate zeroes of analytical functions is applied to prove the existence of, and to specify, thin coatings with vanishing reflectance at isolated frequencies. Coatings much thinner than quarter-wavelength ones are found. Most of the absorption loss takes place close to the cavities and scattering of compressional spherically symmetric waves is important. The viscoelastic shear-wave properties of the rubber are crucial for generating this loss. The requirements for vanishing reflectance are specified using a simplified model with normal plane waves and spherically symmetric waves, that includes effects of multiple scattering among the cavities. An energy relation is derived, relating the anelastic loss in the rubber coating to loss by monopole resonance scattering from isolated cavities. The noticeable effects of multiple scattering are incorporated by a modulating factor.

Superabsorption of acoustic waves with bubble metascreens

“…Calculating the transmission and reflection coe cients for an incident longitudinal wave on such a structure is a complicated matter. Indeed, the coupling between the cavities is too strong to be neglected, and shear waves also need to be taken into account, two factors that make numerical simulations computationally intensive [20,21]. However, a simple model was recently proposed [22] to calculate the transmission and reflection from a single layer of bubbles.…”

Investigation of locally resonant absorption and factors affecting the absorption band of a phononic glass

“…In LRSMs, locally resonant absorption coincides with viscoelastic deformation [11][12][13][14][15][16][17][18]. The sound-absorption region in LRPCs was first found using the multiple-scattering approach; these results showed that a conversion from longitudinal mode to transverse mode near the locally resonant frequencies effectively enhanced the anechoic performance of these materials [7,14].…”

Designing 2D Phononic Crystal Slabs with Transmission Gaps for Solid Angle as well as Frequency Variation

“…As detailed in [17], for example, and references therein, reflection and transmission matrices R B ,T B and R A ,T A can now be introduced, for the discrete set of waves specified by (1)-(3). The mentioned reference concerns the doubly periodic case for a 3D PC, with periodicity in the y direction as well, but the R/T matrix formalism is the same.…”

“…Moroz [21] has published a representation of lattice sums in terms of exponentially convergent series, which has been used in the present work for numerical evaluation of the Θ quantities defined in (17).…”