Theoretical model and analytical approach for a circular membrane–ring structure of locally resonant acoustic metamaterial

Recently developed locally resonant acoustic metamaterials (LRAM) display useful sound attenuation properties over narrow frequency bands. In this study, we present a theoretical model and analytical approach to investigate transmission loss of a circular membrane–ring structure of LRAM. As a degeneration of the ring inner radius being zero, the present model and approach is also suited for acoustic response analysis of the membrane–central-mass structure. Analytical results are compared with the ones from the finite element method to show a quite good agreement. The transmission loss characteristics dependence on the material and geometrical properties of the membrane–ring structure are obtained and discussed. It is indicated that multi-peak transmission loss profile can occur in the membrane–ring structure of LRAM, while the peak transmission loss frequency and bandwidth can be tuned by varying the ring mass location, surface density and ring numbers on the membrane.