An electromechanically coupled zigzag theory is presented for static and free vibration responses in functionally graded material (FGM) plates bonded with piezoelectric layers. It has the capability to consider continuity as well as discontinuity in material properties at all interfaces. The displacement field approximation, which is initially layer based, has been made layer independent by using continuity conditions on displacements and transverse shear stresses as well as zero traction conditions on top and bottom surfaces. Material properties in FGM layers vary continuously in the thickness direction. Piezoelectric layers have constant property across their thickness. Extended Hamilton’s principle for piezoelectric continuum has been used in deriving governing equations of motion and boundary conditions. An analytical solution is obtained for elastic as well as piezoelectric layer bonded FGM plates. Static and free vibration responses have been obtained in a number of FGM plates, with each plate considered to contain a number of FGM layers with discontinuity or continuity in material properties at the interfaces. Wherever available, present responses have been compared with three-dimensional exact solutions and other shear deformation theories. The effects of the aspect ratio, length-to-width ratio, and different schemes for effective material property calculation have been illustrated.

提出了一种机电耦合之字形理论，用于结合压电层的功能梯度材料（FGM）板的静态和自由振动响应。它具有考虑所有界面处材料特性的连续性和不连续性的能力。位移场近似最初是基于层的，通过使用位移和横向剪应力的连续性条件以及顶面和底面的零牵引条件，可以使层近似于层。FGM层中的材料属性在厚度方向上连续变化。压电层在其整个厚度上具有恒定的属性。压电连续体的扩展汉密尔顿原理已用于推导运动和边界条件的控制方程。对于弹性以及压电层粘合的FGM板，可以获得一种分析解决方案。在许多FGM板中已经获得了静态和自由振动响应，其中每个板都包含了许多FGM层，这些FGM层在界面处具有不连续或连续的材料特性。尽可能将当前的响应与三维精确解和其他剪切变形理论进行比较。已经说明了纵横比，长宽比以及有效材料属性计算的不同方案的影响。每个板都包含许多FGM层，这些FGM层在界面处的材料属性不连续或连续。尽可能将当前的响应与三维精确解和其他剪切变形理论进行比较。已经说明了纵横比，长宽比以及有效材料属性计算的不同方案的影响。每个板都包含许多FGM层，这些FGM层在界面处的材料属性不连续或连续。尽可能将当前的响应与三维精确解和其他剪切变形理论进行比较。已经说明了纵横比，长宽比以及有效材料属性计算的不同方案的影响。