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

TLDR

Membrane‑type acoustic metamaterials (MAMs) have shown an unusual ability to control low‑frequency sound transmission and reflection. The study develops an analytical vibroacoustic membrane model to investigate the sound transmission behavior of a MAM under normal incidence. The model represents the MAM as a prestretched elastic membrane with attached rigid masses, employs a point‑matching approach with distributed point forces along the mass–membrane interface to capture finite‑size mass effects, and quantitatively examines how mass weight, size, eccentricity, pretension, and membrane thickness influence transmission peak and dip frequencies. Model predictions agree with finite‑element simulations, uncover new peak and dip frequencies for MAMs with one or multiple eccentric attached masses, and offer an efficient design tool for such metamaterials.

Abstract

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.