Study of bandgap property of a bilayer membrane-type metamaterial applied on a thin plate

This work is aimed to study the bandgap property of a thin plate structure with periodically attached bilayer membrane-type resonators. An analytical method based on the Plane Wave Expansion (PWE) method combined with the Rayleigh method, is proposed to predict the bandgap property of bilayer membrane-type metamaterials. The accuracy of the proposed method is verified by the finite element analysis, and a parametric analysis is conducted to reveal the effect of parameters on the bandgap performance. It is found that such a metamaterial can generate two separated bandgaps through the contribution of its two layers of membranes. It is observed that the increase of membrane tensile stress or the magnitude of attached mass can lead to the broadening of bandgaps, whilst the change of unit cell's periodicity has the opposite effect. In addition, if compared with the corresponding single layer membrane-type metamaterials, it is shown that the bilayer membrane-type's first bandgap is suppressed while the second one is extended. However, by applying proper membrane tensile stress and mass magnitude, the suppression of the first bandgap can be weakened whilst allowing the tuning of the bandgap location. These characteristics reveal the benefits of using bilayer membrane-type metamaterial as it possesses higher agility in bandgap tuning. The proposed method can provide an effective tool for the bilayer membrane-type metamaterial design and optimisation.