Abstract

In the present work, the vibration response of the porous functionally graded piezoelectric plates with electro-thermal loading using finite element formulations has been studied. A sigmoid law is used for the material property deviation along the thickness direction. The first-order shear deformation theory (FSDT) with von Karman nonlinear strains and Hamilton's principle is used to obtain the governing equations. The governing equations are solved by finite element methods with 9-noded iso-parametric rectangular elements with 7 degrees of freedom (DOFs) per node. The accuracy of the results is evaluated by comparing them with the results available in the literature. The analysis shows that the uneven type porosity distribution gives a larger nondimensional frequency than the even type porosity distribution FGP plate. The non-dimensional frequency decreases with increases in the $a/h$ ratio. Among all the conditions, CCCC boundary conditions have a larger frequency than SSSS, SFSF, SFCF, and CFFF. The obtained frequency under applied electric loading depends on the magnitude and the applied voltage sign. As the temperature change $(\Delta T)$ increases with the porosity exponent $(\alpha )$ of the FGP plate, the nondimensional frequency is also increasing. The obtained results can design a porous FGP material-based smart composite structure under a thermo-electric environment.

摘要

在目前的工作中，使用有限元公式研究了电热加载多孔功能梯度压电板的振动响应。沿厚度方向的材料性能偏差采用S形定律。使用冯卡门非线性应变和哈密顿原理的一阶剪切变形理论（FSDT）来获得控制方程。控制方程通过有限元方法求解，采用 9 节点等参数矩形单元，每个节点有 7 个自由度 (DOF)。通过与文献中可用的结果进行比较来评估结果的准确性。分析表明，不均匀型孔隙率分布比均匀型孔隙率分布给出更大的无量纲频率FGP板的孔隙率分布。无量纲频率随着频率的增加而降低$A/H$比率。在所有条件中，CCCC边界条件的出现频率高于SSSS、SFSF、SFCF和CFFF。在施加的电负载下获得的频率取决于大小和施加的电压符号。随着温度的变化$（\Delta \mathrm{时间}）$随孔隙度指数增加$（\alpha ）$FGP板的无量纲频率也在增加。所得结果可在热电环境下设计基于多孔FGP材料的智能复合结构。