Asymmetric sound scattering by gratings of monopolar and dipolar resonators in a viscoelastic materiala

A self-consistent analytical model of a locally resonant coating exhibiting strong asymmetric wave scattering is presented. Gratings of resonant inclusions composed of cavities and hard particles embedded in a soft matrix are translated to the problem of sound scattering by monopolar and dipolar type resonators in a one-dimensional waveguide. Equations of motion for gratings of cavities and hard particles are developed that incorporate added mass, damping, and restoration forces to take into account multiple scattering effects. Expressions for the impedances of the resonators are derived from which the particle velocity fields are obtained. Monopole and dipole strengths are also calculated in terms of polarizability tensor components, which in turn are obtained from a retrieval method. Sound scattering by monopolar and dipolar resonators of different size and distribution within the waveguide are examined. Using detailed understanding of the interaction between groups of resonators, optimized solutions for a new class of acoustic materials can be designed by selecting layers of resonators to produce a given response.