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. (C) 2021 Elsevier Ltd. All rights reserved.

提出了一种结合有限元计算的传递矩阵方法，用于表征具有面内周期性的均匀和非均匀吸声材料。所表征的声学材料主要是由多层构成的超材料，其中至少一层由非均匀材料（NHM）组成。NHM是一种多孔或固体基质，其中嵌入了周期性的简单或复杂夹杂物以及亥姆霍兹共鸣器。通过所提出的类似于三麦克风两负载法的方法确定NHM的等效传递矩阵。通过将NHM的等效传递矩阵与其他传递矩阵进行串联解析耦合，可以在仅使用有限元计算会更加昂贵和耗时的配置中轻松快速地对复杂多层系统进行建模。将本方法预测的法向入射声传输损耗结果与不同超材料配置的有限元结果进行了比较，得到了良好的一致性。所提出的方法为在法向入射下表征和设计具有周期性夹杂物的复杂多层声学超材料提供了一种有效的途径。它可用于优化包含非均匀材料的多层系统。（C）2021爱思唯尔有限公司。保留所有权利。