Abstract

Acoustic Metamaterials comprising a soft medium embedded with a lattice of small scatterers (cavities or hard inclusions) have traditionally been used for exploration of new wave phenomena (wave trapping and localisation, acoustic cloaking, imaging, focusing, filtering). This is due to the strong coupling between the sub-wavelength resonances of individual scatterers (determined by low shear modulus) and the Bragg scattering caused by periodical arrangements of the scatterers.  Multiple scattering of acoustic waves between scatterers in proximity can further strengthen the resonance, leading to enhanced wave manipulation that can block transmission or perfectly absorb sound waves. This becomes important for practical solutions in many maritime applications to control water-born sound. We discuss a number of phenomenological methods that can be used to incorporate multiple-scattering effects in the analytical models of Acoustic Metamaterials with a soft (rubber-like) matrix. These methods heavily employ the well-known analogies and results from electrostatics and diffusion. These analogies stem from the overarching analytical framework of the underlying Laplace equation that can be applied to describe Acoustic Metamaterials at the low-frequency limit (but still above subwavelength resonance of individual scatterers). To validate the assumptions of the theory some numerical results are also presented.