Numerical modelling of finite periodic arrays of acoustic resonators using an efficient 3D BEM model

Abstract Noise abatement provided by acoustic metamaterials is one of the peculiar features presented by these remarkable materials. In fact, the use of local resonant elements and their periodic distribution in the form of so-called sonic crystal arrangements have demonstrated to enhance those attenuation properties. In this work, the authors present an efficient three-dimensional (3D) numerical model based on the Boundary Element Method (BEM) to analyse the acoustic behaviour in the frequency domain of finite periodic arrays of acoustic resonators. Unlike most analytical methods, the proposed model captures the finite features of these systems and their associated effects. Furthermore, usual numerical tools such as the Finite Element Method (FEM) may become impractical because the detailed and complex geometry of these devices would lead to very large discretized spatial domains. Instead, in the proposed model, only the resonators have to be discretized. Actually, an efficient strategy has been devised to adequately take into account the periodicity of the finite array of resonators, resulting in significant savings of computational resources. Additionally, the Adaptive Cross Approximation (ACA) technique is used, further reducing the computational requirements since it is based on hierarchical representation of matrices and allows a very efficient storage of the system matrix.