LAUSR

Abstract Acoustic exterior problems are in this paper solved numerically using the Astley-Leis infinite element method (IFEM). Normal modes can be determined thanks to the frequency independence of the system matrices. Convergence properties of the harmonic sound pressure solution as well as of normal mode eigenvalues are investigated for two-dimensional elliptical computational domains to estimate the essential requirements of accuracy. A relationship between the half-axis ratio of the ellipses and the eigenvalues is identified. By solving half-space problems, symmetry of the computational domains is utilized, which is shown for the first time for frequency-independent normal modes in exterior acoustics. This paper discusses applicability of the modes in the example of sonic crystals—periodic arrays of scatterers, in this context denoted as acoustic meta-atoms—that have recently attracted attention for their possible use as noise barriers. It can be shown that the sound-insulating effect of finite sonic crystals and individual meta-atoms in the free field can be related to normal modes in exterior acoustics. With the help of this approach, the absorption by Helmholtz resonators and due to a boundary admittance inside are studied. This work provides a new point of view and physical insights into the effects and underlying physics of sound insulation by finite sonic crystals and acoustic meta-atoms in free field. Although it is not the intention of this article to optimize the arrays, the method of normal modes in exterior acoustics is presented as an appropriate and novel tool for their dimensioning and design.