In this paper, a localized meshless collocation method, the generalized finite difference method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic waves in 2D solid phononic crystals with square and triangular lattice. The corresponding theoretical consistency analysis of the GFDM is given. The universal algorithm for the uniform/scattered node generation in the GFDM is presented. In comparison with the traditional plane wave expansion (PWE) method and Pressure Acoustics Module in COMSOL software, the proposed GFDM can provide the similar accurate results with less computational times for calculating the band structures of the simple/complicated shape scatterers in the square/triangular lattice. Three influence factors (Filling fractions (Ff), rotation angles (Ra) and arm widths (Aw) in the unit-cell) of the bandgap properties in 2D phononic crystals are numerically discussed.

本文首先采用局部无网格配点法，即广义有限差分法（GFDM）来计算具有正方形和三角形晶格的二维固体声子晶体中反平面横向弹性波的带隙。给出了GFDM的相应理论一致性分析。提出了在GFDM中统一/分散节点生成的通用算法。与COMSOL软件中的传统平面波扩展（PWE）方法和压力声学模块相比，所提出的GFDM能够以较少的计算时间提供相似的准确结果，从而可以计算出简单/复杂形状散射体在正方形/三角形中的能带结构格子。三个影响因素（填充分数（Ff），