An approximate analytical model is presented to investigate sound transmission, reflection and absorption of a rubber-like medium comprising a single layer of periodic cylindrical voids attached to a steel backing. The layer of voids is modelled as a homogeneous medium with effective material and geometric properties. A numerical model based on the finite element method is developed to validate results from the homogenization model, as well as to show further insights into the physical mechanisms associated with the system acoustic performance. Monopole resonance of the voids is shown to reduce sound transmission through the voided medium due to increased reflection, resulting in poor sound absorption around this frequency. Peaks of high sound absorption are attributed to Fabry–Pérot resonance with the frequency of the first peak derivable by a lumped spring-mass analogy. Sound absorption for a single layer of voids in a soft elastic medium with a steel backing is shown to be similar to the sound absorption in the same elastic medium but without the steel backing, for a single layer of voids and its mirror image in the direction of sound propagation.

A metasurface comprising cavities in a soft medium has been proven to be highly efficient for control of water-borne sound waves. We formulate an analytical model to predict the acoustic performance of a soft elastic medium embedded with disk-shaped cavities and submerged in water. Each layer of cavities is approximated as an effective boundary that incorporates the effect of multiple scattering of waves and accounts for different damping mechanisms. The results from our analytical model are compared with numerical and experimental results from the literature.

We present an analytical framework to investigate the acoustic performance of an array of closely spaced spherical cavities embedded in a thin soft medium submerged in water. Each layer of cavities is approximated as a homogenized layer with effective properties. Strong monopole resonance of the cavities and multiple scattering of waves between cavities in proximity are taken into account. Analytical results for the metasurface with and without a rigid backing are compared with numerical simulations as well as with experimental results from the literature.