In this study, the effects of the variable nonlocal parameters on the free vibration of power-law and sigmoid functionally graded nanoplates are investigated using a simple inverse hyperbolic shear deformation theory incorporating with nonlocal elasticity theory. The novelty of this study is that the nonlocal parameter is assumed to vary smoothly through the thickness of the functionally graded nanoplates. The governing equations of motion are established using the variation form of Hamilton's principle, and they are solved via Navier's closed-form solution. Some verification studies are carried out to demonstrate the accuracy and efficiency of the proposed algorithm in predicting the free vibration behavior of functionally graded nanoplates. The effects of some parameters such as the aspect ratio, the side-to-thickness ratio, the power-law index as well as the variation of the nonlocal parameters are also considered carefully. The results show that the variation of the nonlocal parameter plays significant effects on the free vibration response of the functionally graded nanoplates. The influence of the nonlocal parameters on the free vibration of various kinds of functionally graded nanoplates is completely different, it depends on the variation of the material ingredients across the thickness of the functionally graded nanoplates.

在这项研究中，使用结合非局部弹性理论的简单反双曲剪切变形理论研究了可变非局部参数对幂律和 sigmoid 功能梯度纳米板的自由振动的影响。这项研究的新颖之处在于假设非局部参数在功能梯度纳米板的厚度上平滑变化。执政的利用哈密顿原理的变分形式建立运动方程，并通过纳维尔闭式解法求解。进行了一些验证研究，以证明所提出的算法在预测功能梯度纳米板的自由振动行为方面的准确性和效率。还仔细考虑了一些参数的影响，如纵横比、边厚比、幂律指数以及非局部参数的变化。结果表明，非局部参数的变化对功能梯度纳米板的自由振动响应有显着影响。非局部参数对各种功能梯度纳米板自由振动的影响是完全不同的，