Within a framework of the state space method, an axisymmetric solution for functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate is presented in this paper. Applying the finite Hankel transform onto the state space vector, an ordinary differential equation with constant coefficients is obtained for the circular plate provided that the free boundary terms are zero and an exponential function distribution of material properties is assumed. The ordinary differential equation is then used to obtain the stress, displacement and electric components in the physical domain of the elastic simply supported circular plate through the use of the propagator matrix method and the inverse Hankel transform. The numerical studies are carried out to show the validity of the present solution and reveal the influence of material inhomogeneity on the axisymmetric bending of the circular plate with different layers and loadings, which provides guidance for the design and manufacture of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate.

中文翻译：

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功能梯度一维六方压电准晶圆板轴对称弯曲分析

在状态空间方法的框架内，本文提出了功能梯度一维六方压电准晶圆板的轴对称解。将有限Hankel变换应用到状态空间向量上，假设自由边界项为零并假设材料特性呈指数函数分布，则得到圆板的常系数常微分方程。然后通过传播子矩阵法和Hankel逆变换，利用常微分方程得到弹性简支圆板物理域中的应力、位移和电分量。