This work focuses on the free vibration characteristics of the functionally graded piezoelectric (FGPE) plate with classical and elastic constraints. First, the analytical model is established for the FGPE plate on the basis of the first-order shear deformation theory (FSDT). Besides, different distribution profiles of the material constituent are considered for the FGPE plate model, and various external initial voltages are also considered for modeling the piezoelectric effect. The displacement functions for the FGPE plate are then given in the form of third-kind orthogonal polynomials. Ultimately, the solution of the FGPE plate model is resolved by means of the Ritz method. Convergence and accuracy of the presented model are verified, and a series of parametric investigations are given.

这项工作侧重于具有经典和弹性约束的功能梯度压电 (FGPE) 板的自由振动特性。首先，基于一阶剪切变形理论（FSDT）建立了FGPE板的解析模型。此外，FGPE 板模型考虑了材料成分的不同分布曲线，并且还考虑了各种外部初始电压来模拟压电效应。然后以第三类正交多项式的形式给出 FGPE 板的位移函数。最终，通过 Ritz 方法求解 FGPE 板模型的解。验证了所提出模型的收敛性和准确性，并给出了一系列参数研究。