In the present study, static and free vibration analysis of single walled functionally graded carbon nano-tube (CNTs) reinforced composite plate is carried out in the framework of trigonometric shear deformation theory. Trigonometric shear deformation theory full fills the traction free boundary condition at the top and bottom of the plate due to which it does not require shear correction factor. The Hamilton’s principle is used to derive governing differential equations and the Navier’s solution technique is used to obtain closed-form solution. The analytical approach is used to analyse the effect of the different span thickness ratios, volume fraction of CNTs, and distribution of CNTs on the deflection, stresses, natural frequencies, and corresponding mode shapes of CNTs reinforced composite plate. Four different types of CNTs reinforcement distribution such as, uniformly distribution (UD) and three types of functionally graded (FG) i.e. FG-O, FG-X and FG-V are selected here for the analysis. Here, the efforts are made to achieve the best possible arrangement for the reinforcement distribution that will produce the improved static and free vibration responses for the functionally graded CNTs reinforced composite plate.

在本研究中，在三角剪切变形理论的框架下进行了单壁功能梯度碳纳米管（CNTs）增强复合板的静，自由振动分析。三角剪切变形理论完全填补了板顶部和底部的牵引自由边界条件，因此不需要剪切校正因子。使用汉密尔顿原理导出控制微分方程，使用纳维尔解法获得封闭形式的解。该分析方法用于分析不同跨距厚度比，碳纳米管的体积分数以及碳纳米管的分布对碳纳米管增强复合板的挠度，应力，固有频率以及相应的模态形状的影响。在此选择四种不同类型的CNT增强分布，例如均匀分布（UD）和三种功能梯度（FG），即FG-O，FG-X和FG-V。在此，我们努力为增强材料的分布提供最佳的布置，从而为功能梯度的CNTs增强复合材料板带来改善的静态和自由振动响应。