关键词： 声子晶体, 孔洞几何形状, 傅里叶系数, 无量纲最小韧带宽度, 带隙, 有限元分析

Abstract: To reveal the influence mechanism of hole geometry on the bandgap characteristics of two-dimensional porous phononic crystals,a parametrically describable hole geometric model was constructed based on Fourier coefficients,and the band structures corresponding to different geometric models were calculated through finite element method.The effects of low-order Fourier coefficients (c₁,c₂),the dimensionless minimum ligament width (h/L),and high-order Fourier coefficients (c₃,c₄) on the relative bandgap width were systematically analyzed.The results indicate that h/L and c1 are the two core parameters determining the relative bandgap width;decreasing h/L and increasing c1 can both effectively broaden the relative bandgap.Low-order Fourier coefficients c₁ primarily regulate the overall hole morphology and play a decisive role in tuning the relative bandgap width,while high-order Fourier coefficients _c3 and c₄ mainly modify the local detailed features of the hole and have a limited effect on the relative bandgap width.This suggests a clear intrinsic correlation between hole shape parameters and the bandgap characteristics of phononic crystals.

Key words: phononic crystal, hole geometries, Fourier coefficients, dimensionless minimum ligament width, band gap, finite element analysis