  Membrane-type Acoustic Metamaterials (MAMs) have demonstrated unusual
capacity in controlling low-frequency sound transmission/reflection. In this
paper, an analytical vibroacoustic membrane model is developed to study sound
transmission behavior of the MAM under a normal incidence. The MAM is composed
of a prestretched elastic membrane with attached rigid masses. To accurately
capture finite-dimension rigid mass effects on the membrane deformation, the
point matching approach is adopted by applying a set of distributed point
forces along the interfacial boundary between masses and the membrane. The
accuracy and capability of the theoretical model is verified through the
comparison with the finite element method. In particular, microstructure
effects such as weight, size and eccentricity of the attached mass, pretension
and thickness of the membrane on the resulting transmission peak and dip
frequencies of the MAM are quantitatively investigated. New peak and dip
frequencies are found for the MAM with one and multiple eccentric attached
masses. The developed model can be served as an efficient tool for design of
such membrane-type metamaterials.
