Due to the limit of preparation technology, defects, such as cracks and inclusions, are inevitable in the functionally graded quasi‐crystal material. For the purpose of the guided wave non‐destructive testing on the functionally graded (FG) two‐dimensional(2‐D) hexagonal quasi‐crystal(QC) plates, Lamb and SH wave characteristics in the context of the Bak's model are investigated by means of the Legendre polynomial method. The convergence of the polynomial method applied on the FG 2‐D hexagonal QC plate is analyzed. Some new wave characteristics resulted from the phonon‐phason coupling effect are revealed. There are three Lamb‐like modes without cut‐off frequencies for the x‐y and y‐z QC plates, but four Lamb‐like modes without cut‐off frequencies for the x‐z QC plate. For phonon modes, phonon displacements and stresses are bigger than phason displacements and stresses. However, they are just opposite for phason modes. It can be utilized to distinguish phonon modes and phason modes.

中文翻译：

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功能梯度二维六角形准晶板中的导波特性

由于制备技术的限制，在功能梯度的准晶体材料中不可避免地会出现裂纹和夹杂物等缺陷。为了对功能梯度（FG）二维（2-D）六角形准晶体（QC）板进行导波无损检测，研究了Bak模型背景下的Lamb和SH波特性勒让德多项式方法的平均值。分析了应用于FG二维六角形QC板的多项式方法的收敛性。揭示了声子-声子耦合效应产生的一些新的波特征。x y和yz QC板有三种没有截止频率的Lamb-like模式，但对于x - y和y-z QC板有四种没有截止频率的Lamb-like模式。x ‐ z QC板。对于声子模式，声子的位移和应力大于声子的位移和应力。但是，它们在相子模式下正好相反。它可以用来区分声子模式和声子模式。