Design method of acoustic metasurface based on analytical scaling laws for one-octave near-perfect sound absorption

Abstract

This paper presents a generalized design method based on analytical scaling laws for acoustic metasurfaces (AMS) to achieve one-octave near-perfect sound absorption. Previous numerical studies suggested that the optimal area ratio of unit cells follows a power law of the frequency ratio, but the theoretical background remained empirical. In this study, we derive the optimal scaling law of the area ratio analytically by introducing physical correction terms into the classical Helmholtz resonance theory, accounting for the wave propagation effect in the back cavity and the viscous boundary layer effect in the neck. The proposed formulation, σ_assy,i ∝ f_i^−(1.5+ϵ), successfully explains the varying power indices observed in different unit cell geometries. Numerical validation across multiple target frequencies confirms the universality of this scaling-law-based design method within a one-octave bandwidth. By eliminating the need for computationally expensive heuristic optimization algorithms, this practical framework provides a straightforward engineering tool for developing highly efficient acoustic absorbers.