This article presents the free vibration frequencies of composite plates reinforced with single-walled carbon nanotubes by using a refined simplified two-variable nth-higher-order theory. Four kinds of distribution of uniaxially aligned reinforcement material are presented. The most famous one is the uniform; in addition, three types of functionally graded distributions of carbon nanotubes in the through-thickness direction of the plates are investigated. The effective physical properties of composite media are given according to a refined rule of mixtures approach that contains the efficiency parameters. Exact closed-form formulation based on a refined simplified two-variable nth-higher-order plate theory that can be adapted to the vibration of such plates is investigated. Accuracy of presented approach is validated by comparing its results with those given by other investigators

中文翻译：

---

碳纳米管增强板的振动基于改进的n阶高阶理论

本文通过使用简化的简化的二变量n次高阶理论，介绍了用单壁碳纳米管增强的复合板的自由振动频率。提出了单轴排列的增强材料的四种分布。最著名的是制服；此外，研究了碳纳米管在板的整个厚度方向上的三种功能梯度分布。复合材料的有效物理特性是根据包含效率参数的混合方法的精确规则给出的。基于精简的简化二变量n的精确闭式公式研究了可以适应这种板的振动的高阶板理论。通过比较其结果与其他研究者给出的结果，验证了所提出方法的准确性