“…In recent years, researchers have made a significant progress in the development of calculation methods to analyze the band gap structure of phononic crystals. At present, the commonly used methods are: plane wave expansion method (PWE) (Zuo et al, 2022), lumped mass method (Kong et al, 2023), finite difference time domain (FDTD) method (Cao et al, 2004), finite element method (FEM) (Lu et al, 2022). As a mature method for numerical simulation of mechanical systems, the finite element method has a worked well with periodic structures and has also been successfully applied to the calculation of one-, two-and three-dimensional structures.…”