Propagation of torsional waves in a thin circular plate of generalized phononic crystals

By introducing periodicity in the direction of variable vectors, the concept of existing phononic crystals (PCs) is expanded to generalized phononic crystals (GPCs), and a one-dimensional thin circular plate of GPCs (GPC plate) consisting of two alternating homogeneous materials is constructed. To show the characteristics of a torsional stress wave propagating along the radial direction, a transfer matrix is derived based on the basic torsional wave equation of the thin circular plate in cylindrical coordinates. A localization factor is introduced to evaluate the average attenuation of torsional stress waves in the structure, thus the band gaps are calculated. The inherent relationships between wave attenuation band, wave front and periodicity are discussed in detail. Finite element method simulations, numerical analyses and the insertion loss method are combined to investigate the effects of the main parameters on the torsional stress wave band in GPC plate. The results show that there are significant band gaps of the torsional stress waves caused by the periodicity of GPC plate, which are similar to those of existing PCs, and the localization factor can be used for the wave analysis of GPCs. In addition, structural and material parameters have a great influence on the wave attenuation band of the GPC plate.