In this research, an analytical solution is presented for the functionally graded piezoelectric cylindrical variable wall thickness that is subjected to mechanical and electrical loading. The non-homogeneous distribution of materials is considered as a power function. The first-order electric potential theory, first-order shear deformation theory, and the energy method are used for extracting the system of governing equations. The solution is accomplished using the matched asymptotic expansion method of the perturbation technique. The effects of non-homogeneous properties on the electromechanical are discussed. Since the intensity of variations in the distribution of properties in functionally graded piezoelectric cylinders can be changed using non-homogeneity constant, the electromechanical behavior of the cylinder can be changed by non-homogeneity constant. By reducing the electric or displacement field in functionally graded piezoelectric cylinders, de-polarization or loss of piezoelectric properties may be averted. Results indicate that non-homogeneity constant has a significant effect on the electromechanical behavior. However, in some cases, the effects of non-homogeneity constant may be neglected. Comparing these results with those predicted by the plane elasticity theory and finite element method shows good agreement. In fact, the present solution can be considered as an objective function to optimize the properties and behavior.

中文翻译：

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使用一阶电势理论和微扰技术对功能梯度压电可变厚度圆柱壳进行电弹性分析

在这项研究中，针对承受机械和电气载荷的功能梯度压电圆柱可变壁厚提出了一种解析解。材料的非均匀分布被视为幂函数。一阶电势理论、一阶剪切变形理论和能量法用于提取控制方程组。该解是使用微扰技术的匹配渐近展开方法完成的。讨论了非均匀特性对机电的影响。由于功能梯度压电圆柱中特性分布的变化强度可以使用非均匀常数来改变，气缸的机电行为可以通过非均匀常数来改变。通过减少功能梯度压电圆柱体中的电场或位移场，可以避免去极化或压电特性的损失。结果表明，非均匀性常数对机电行为有显着影响。然而，在某些情况下，非均匀常数的影响可能会被忽略。将这些结果与平面弹性理论和有限元方法预测的结果进行比较显示出良好的一致性。事实上，本解决方案可以被视为优化属性和行为的目标函数。结果表明，非均匀性常数对机电行为有显着影响。然而，在某些情况下，非均匀常数的影响可能会被忽略。将这些结果与平面弹性理论和有限元方法预测的结果进行比较显示出良好的一致性。事实上，本解决方案可以被视为优化属性和行为的目标函数。结果表明，非均匀性常数对机电行为有显着影响。然而，在某些情况下，非均匀常数的影响可能会被忽略。将这些结果与平面弹性理论和有限元方法预测的结果进行比较显示出良好的一致性。事实上，本解决方案可以被视为优化属性和行为的目标函数。