Multiple band gaps of two-dimensional elastic metamaterials with self-similar hierarchy

Abstract Elastic metamaterials with band gaps can block the transmission of elastodynamic waves and have wide applications in life and industry. Wide band gaps and low-frequency band gaps are the two goals of research on elastic metamaterials with band gaps. In this study, two models of two-dimensional elastic metamaterials with self-similar hierarchies were designed. The models were obtained by replacing the arms in the unit cell with composite structures. There is a wide band gap and low-frequency band gap for each unit cell with second-order replacement. The influence of the geometric dimensions of the arms on the properties of the band gaps was also studied. The properties of the band gaps can be altered by changing the arm dimensions. Vibration analyses based on the finite element method (FEM) were conducted for materials with improved unit cells to verify the existence of band gaps. Metamaterials can be applied in many cases to reduce or isolate noise and vibrations.