Towards optimal design of locally resonant acoustic metamaterials

The paper presents an in-depth analysis of solid locally resonant acoustic metamaterials (LRAMs) consisting of rubber-coated inclusions. Dispersion properties of two-dimensional LRAMs are studied by means of finite-element modal analysis. For an incompressible rubber, only one practically important spectral band gap is found for in-plane modes in a low-frequency range. This result is in striking contrast with the compressible coating case, previously studied in the literature. For inclusions with a circular cross-section, the lower bound of the band gap can be evaluated exactly by means of the derived analytical solution, which is also valid for compressible coatings and can therefore be used to determine lower bounds of higher band gaps as well. The influence of geometric and material parameters, filling fraction and inclusion shape on the width of the lowest band gap is investigated in detail. Based on the results of this analysis, an optimal microstructure of LRAMs yielding the widest low-frequency band gap is proposed. To achieve the band gap at the lowest possible frequencies in LRAMs suitable for practical applications, the use of the tungsten core material is advised, as a safe and economically viable alternative to commonly considered lead and gold. Two configurations of LRAM with various sizes of coated tungsten cylindrical inclusions with circular cross-section are considered. The evolution of dispersion spectra due to the presence of different inclusions is investigated, and the parameters for optimal design of LRAMs are determined.