A new shear deformation theory is introduced to conduct free vibration analysis of the functionally graded plates with simply supported boundary conditions. The shear functions presented in this study vary with gradient index and satisfy the stress-free boundary conditions on the top and bottom surfaces of functionally graded plates without using any shear correction factor. The displacement field is expressed as undetermined integral terms. The governing differential equation and boundary conditions are derived based on Hamilton's principle. The material properties of the functionally graded plates discussed in this paper are assumed to vary through the thickness according to the power-law distribution and the Mori-Tanaka scheme. The amplitude-frequency relationships of the FGM plates are presented and compared with the exsiting results and the obtained numerical results are compared with other 2D and quasi-3D solutions to verify the accuracy and efficiency of the present theory.

引入了一种新的剪切变形理论，以简单支持的边界条件对功能梯度板进行自由振动分析。在这项研究中提出的剪切函数随梯度指数而变化，并且在不使用任何剪切校正因子的情况下满足了功能梯度板的顶部和底部表面的无应力边界条件。位移场表示为不确定的积分项。该控制微分方程边界条件是根据汉密尔顿原理导出的。假定本文讨论的功能梯度板的材料特性会根据幂律分布和Mori-Tanaka方案在整个厚度范围内变化。给出了FGM板的振幅-频率关系，并将其与现有结果进行比较，并将所得数值结果与其他2D和准3D解决方案进行比较，以验证本理论的准确性和有效性。