Vibration band gap characteristics of two-dimensional functionally graded grids using the spectral element method

In this article, the band gap characteristics of two-dimensional periodic grid structures composed of functionally graded materials are studied. According to the first-order shear deformation theory and the spectral element method, the motion equation of the functionally graded beam is established at first, and then the spectral stiffness matrix of the lattice structure is assembled through the coordinate transformation matrix. With the aid of the Bloch theorem, the in-plane wave dispersion relation of periodic grid structures composed of two functionally graded materials is analyzed. The availability and accuracy of the band gap calculation method are verified by structural vibration transmission results based on the finite element method. In addition, the influence of the material parameters of the structure on the dispersion relation of the in-plane wave is obtained. The results extend the range of research on two-dimensional grids which can be applied to the design of filters.