Efficient Fourier-acoustic modeling of evanescent wave effects in metasurface absorbers with arbitrarily shaped elements

Abstract

This work presents a simple and efficient computational approach for the design and analysis of planar acoustic metasurface absorbers, grounded in the principles of Fourier acoustics. The method accommodates various configurations, including periodically or mirror-symmetrically arranged rectangular super-cells, as well as single cells terminating rigid-walled ducts with rectangular or circular cross-sections. Each metasurface (super-)cell may comprise arbitrarily shaped elements characterized by specified input acoustic impedances. A key feature of the model is its unified formulation across all considered geometries, incorporating one frequency-dependent function, which captures the influence of evanescent mode excitation and associated coupling effects. This function is computed from the spectra of characteristic functions describing the geometry, using the Fast Fourier Transform, Discrete Cosine Transform, or numerical integration depending on the symmetry and (super-)cell shape. The approach is demonstrated on micro-perforated panel absorbers backed by multiple resonant cavities, achieving broadband and uniform sound absorption. The model’s efficiency enables parameter optimization, and its predictions are validated against finite element method simulations. Results highlight the critical importance of accounting for evanescent modes in the design process to avoid performance degradation. The proposed method provides a versatile, accurate, and computationally efficient tool suitable for practical applications in noise control, acoustic device design, and architectural acoustics. Implementation MATLAB code is available on https://github.com/MilanCervenka/EvanescentFourier.