Flexural vibration band gaps of the multiple local resonance elastic metamaterial plates with irregular resonators

Abstract

This paper presents the modeling technique, design method, a new working way and influence factors for elastic metamaterial plates. Two kinds of new elastic metamaterials plates with local resonators are designed. The band structure and transmission spectrum are calculated by finite element method (FEM). The formation mechanism of the bending vibration band gap is further analyzed by the displacement field of the band gap and the dynamic effective dislocation density of the metamaterial plate. Compared with regular shapes, irregular shapes of oscillators and rubber are easier to open bending band gaps. The effects of the geometrical parameters on the flexural vibration band gaps (FVBGs) are studied in detail. The related results can well confirm that the two novel types of local resonators illustrate the vibration characteristics of the two-degree-of-freedom system during the vibration, and two obvious FVBGs can be found in low frequency. The double-side metamaterial plates can broaden the width of FVBGs. The installation angles have no effect on the dispersion curves of the double-side metamaterial plates.