In this study, we investigate the induction field and the phonon and phason stress fields of a spheroidal inclusion embedded within an infinite matrix of a one-dimensional (1D) hexagonal piezoelectric quasicrystal subjected to the following three prescribed uniform traction boundary conditions: axisymmetric loading, out-of-plane and in-plane shear. The explicit expressions are derived in the surrounding matrix and the inclusions by setting the correct potential function. The reduced results show that the stresses exhibit a singularity on the crack faces. The obtained results can also serve as a reference for exploring other 1D piezoelectric quasicrystals reinforced by spheroidal inclusions.

中文翻译：

---

一维六角形压电准晶体中的球状夹杂物

在这项研究中，我们研究了在以下三个规定的均匀牵引力边界条件下，嵌入一维（1D）六角形压电准晶体无限矩阵中的球形夹杂物的感应场以及声子和声子应力场。平面外和平面内剪切。通过设置正确的势函数在周围的矩阵和包含物中导出显式表达式。减少的结果表明应力在裂纹面上表现出奇异性。所得结果也可为探索球状夹杂物增强的其他一维压电准晶体提供参考。