In this paper, we study a size-dependent functionally graded piezoelectric (FGP) plate model based on the combination of the modified couple stress and nonlocal elasticity theories, named nonlocal modified couple stress theory (NMCS). Continues variation of the material properties (chosen from PZT family) through the thickness of the plate is considered according to the power law distribution. Employing Hamilton's principle via thin plate theory, we obtain governing equations of motion for two cases: 1) using only the nonlocal parameter for stress tensor, 2) using the nonlocal parameter for both stress and couple stress tensors. Navier's approach has been used to investigate free vibration of FGP under simply supported edge conditions, analytically. In the first step, we compare our results with the obtained results for the vibration of FGP in the previous studies using the modified couple stress theory and nonlocal elasticity theory, separately. Then, the effects of the aspect ratio, the length of the plate, the side to thickness ratio, FG power index, mode numbers, and the nonlocal and length scale parameters on normalized natural frequencies are investigated.

在本文中，我们基于修正偶应力和非局部弹性理论的组合，研究了尺寸相关的功能梯度压电（FGP）平板模型，称为非局部修正偶应力理论（NMCS）。根据功率定律分布，可以考虑通过板的厚度持续变化材料特性（从PZT系列中选择）。利用汉密尔顿原理通过薄板理论，我们获得了两种情况下的运动控制方程：1）仅对应力张量使用非局部参数，2）对应力和偶应力张量使用非局部参数。Navier的方法已用于分析FGP在简单支撑边缘条件下的自由振动。在第一步中 我们分别使用改进的耦合应力理论和非局部弹性理论，将我们的结果与FGP振动获得的结果进行比较。然后，研究了纵横比，板的长度，边与厚度的比，FG功率指数，模式编号以及非局部和长度比例参数对归一化固有频率的影响。