Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: Plate model

TLDR

The paper develops a theoretical vibroacoustic plate model to uncover the sound‑energy absorption mechanism of membrane‑type acoustic metamaterials under normal incidence. The model employs a plate formulation with point matching to solve a coupled vibroacoustic integrodifferential equation, capturing membrane strain energy from resonant and antiresonant mass motion and analyzing microstructural effects such as mass eccentricity, membrane depth, thickness, and loss factor on absorption peaks. The MAM, accounting for membrane dissipation, acts as a super absorber of low‑frequency sound, with absorption quantified and validated against finite‑element predictions.

Abstract

By considering the elastic membrane's dissipation, the membrane-type acoustic metamaterial (MAM) has been demonstrated to be a super absorber for low-frequency sound. In the paper, a theoretical vibroacoustic plate model is developed to reveal the sound energy absorption mechanism within the MAM under a plane normal incidence. Based on the plate model in conjunction with the point matching method, the in-plane strain energy of the membrane due to the resonant and antiresonant motion of the attached masses can be accurately captured by solving the coupled vibroacoustic integrodifferential equation. The sound absorption ability of the MAM is quantitatively determined, which is also in good agreement with the prediction from the finite element method. In particular, microstructure effects including eccentricity of the attached masses, the depth, thickness, and loss factor of the membrane on sound absorption peak values are discussed.