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Membrane-type Acoustic Metamaterials (MAMs) have demonstrated unusualcapacity in controlling low-frequency sound transmission/reflection. In thispaper, an analytical vibroacoustic membrane model is developed to study soundtransmission behavior of the MAM under a normal incidence. The MAM is composedof a prestretched elastic membrane with attached rigid masses. To accuratelycapture finite-dimension rigid mass effects on the membrane deformation, thepoint matching approach is adopted by applying a set of distributed pointforces along the interfacial boundary between masses and the membrane. Theaccuracy and capability of the theoretical model is verified through thecomparison with the finite element method. In particular, microstructureeffects such as weight, size and eccentricity of the attached mass, pretensionand thickness of the membrane on the resulting transmission peak and dipfrequencies of the MAM are quantitatively investigated. New peak and dipfrequencies are found for the MAM with one and multiple eccentric attachedmasses. The developed model can be served as an efficient tool for design ofsuch membrane-type metamaterials.

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