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

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.