Characterization and development of periodic acoustic metamaterials using a transfer matrix approach

A transfer matrix approach that combines with finite element calculations is proposed to characterize homogeneous and non-homogeneous acoustic absorbing materials with in-plane periodicity. The characterized acoustic materials are mainly metamaterials made of multiple layers, where at least one layer consists of a non-homogeneous material (NHM). The NHM is a porous or solid matrix with embedded periodic simple or complex inclusions and Helmholtz resonators. The equivalent transfer matrix of the NHM is determined by the proposed approach which is similar to the three-microphone two-load method. By using the equivalent transfer matrix of the NHM coupled analytically in series with other transfer matrices, complex multilayer systems can be modeled easily and quickly in configurations wherein the use of finite element calculation alone will be more expensive and time consuming. The results of the normal incidence sound transmission loss predicted by the present method are compared with finite element results for different configurations of metamaterials and good agreements are obtained. The proposed method offers an efficient way to characterize and design at normal incidence complex multilayer acoustic metamaterials with periodic inclusions. It can be used to optimize multilayer system containing non-homogeneous materials.