Calculation Of Band Structure Of Two-Dimensional Phononic Crystals By The Local Radial Basis Function Collocation Method In Time Domain

As a promising periodic structure composite material,phononic crystals have also received a lot of attention.The rapid calculation of the band structures of phononic crystals is an important means to study phononic crystals.In practical engineering,the band structure of many phononic crystals can’t be directly expressed by frequency,so it needs to be calculated based on time discretion.In this paper,the local radial basis function collocation method(LRBFCM)is combined with Houbolt’s time discrete method to establish a numerical analysis method for elastic wave propagation in two-dimensional periodic structures.The local radial basis function collocation method for calculating energy band structure in time domain is studied deeply.The specific studies are as follows:(1)This paper considers the influence of different excitation point sizes and positions on the calculation results of the band structure.Based on the Fourier transform,a time domain to frequency domain analysis tool is established.The boundary wave vector of the first Brillouin zone is considered to obtain the band structure.The influence of numerical techniques on the results is discussed.(2)The band structure calculation of anti-plane phononic crystal and in-plane mixed wave phononic crystal is considered respectively,and the phononic crystal with triangular lattice and square lattice is calculated respectively.The effects of different time step and different coordination nodes on the numerical results are discussed.The influence of different components on the band structure of phononic crystals is considered.(3)Based on the developed numerical model,the accuracy and efficiency of LRBFCM were verified by the numerical calculation results of the COMSOL finite element method.And it is also applied to calculate the band structure of twodimensional plane/anti-plane phononic crystals with different acoustic impedance mismatches,material combinations,scatterer shapes,and lattice forms.The effects of geometrical and material parameters on the energy band structure,especially the energy band gap,of two-dimensional phononic crystals are studied and discussed.