Due to the high brittleness, cracks, holes, and other defects that are easily generated in quasi-crystal structures can affect safe applications in serious cases. For guided wave non-destructive testing, the propagation of Lamb and SH waves in functionally graded one-dimensional hexagonal quasi-crystal plates are investigated. Governing equations of wave motion in the context of Bak’s model are deduced and solved by the Legendre orthogonal polynomial method. Dispersion curves, phonon and phason displacement, and stress distributions are illustrated. The convergence of the present method applied to functionally graded quasi-crystal plates is verified. Moreover, the influences of the phonon-phason coupling effect and graded fields on wave characteristics are analyzed. Some new results are obtained: angular frequencies of phason modes always decrease as phonon-phason coupling coefficients, Ri, increase; and phonon and phason displacements of Lamb and SH waves at high frequencies are mainly distributed in the region that contains more quasi-crystal material with a smaller elasticity modulus and less rigidity. The obtained results establish the theoretical foundation of guided wave non-destructive testing for functionally graded quasi-crystal plates.

由于高脆性，准晶体结构中容易产生的裂纹，孔洞和其他缺陷会严重影响安全应用。对于导波无损检测，研究了Lamb和SH波在功能梯度一维六角形准晶体板中的传播。利用勒让德正交多项式方法推导和求解了在巴克模型的上下文中波动运动的控制方程。示出了色散曲线，声子和声子位移以及应力分布。验证了本方法应用于功能梯度准晶体板的收敛性。此外，分析了声子-声子耦合效应和梯度场对波动特性的影响。获得了一些新结果：R i增加；Lamb波和SH波在高频处的声子和声子位移主要分布在包含更多具有较小弹性模量和较低刚性的准晶体材料的区域。所得结果为功能梯度准晶板的导波无损检测奠定了理论基础。