Acoustic Properties of Surfaces Covered by Multipole Resonators

Abstract

Different types of resonators are used to create acoustic metamaterials and metasurfaces. Recent studies focused on the use of multiple resonators of the dipole, quadrupole, octupole, and even hexadecapole types. This paper considers the theory of an acoustic metasurface, which is a flat surface with a periodic arrangement of multipole resonators. The sound field reflected by the metasurface is determined. If the distance between the resonators is less than half the wavelength of the incident plane wave, the far field can be described by a reflection coefficient that depends on the angle of incidence. This allows us to characterize the acoustic properties of the metasurface by a homogenized boundary condition, which is a high-order tangential impedance boundary condition. The tangential impedance depending on the multipole order of the resonators is introduced. In addition, we analyze the sound absorption properties of these metasurfaces, which are a critical factor in determining their performance. The paper presents a theoretical model for the subwavelength case that accounts for the multipole orders of resonators and their impact on sound absorption. The maximum absorption coefficient for a diffuse sound field, as well as the optimal value for the homogenized impedance, are calculated for arbitrary multipole orders. The examples of the multipole resonators, which can be made from a set of Helmholtz resonators or membrane resonators, are discussed as well.