In this study, free vibration and buckling behaviors of a functionally graded nanoplate supported by the Winkler–Pasternak foundation using a nonlocal classical plate theory are investigated. Eringen’s nonlocal differential model has been used for considering the small-scale effect. The properties of the functionally graded nanoplate are considered to vary transversely following the power law. The governing vibration and buckling equations of an elastically supported functionally graded nanoplate have been derived using the principle of virtual work, and the solution is obtained using the Rayleigh–Ritz method and characteristic polynomials. The advantage of this method is that it disposes of all the drawbacks regarding edge constraints. The objective of the article is to see the effect of edge constraints, aspect ratios, material property exponent, nonlocal parameter, and foundation parameters on the nondimensionalized frequency and the buckling load of an embedded functionally graded nanoplate in a thermal environment. The study highlights that the nonlocal effect is pronounced for higher modes and/or higher aspect ratios and need to be considered for the analysis of the nanoplate. Further, it is observed that the effect of the Pasternak foundation is prominent on nondimensionalized frequencies and buckling of the functionally graded nanoplate.

在这项研究中，使用非局部经典板理论研究了由Winkler-Pasternak基础支撑的功能梯度纳米板的自由振动和屈曲行为。Eringen的非局部差分模型已用于考虑小规模效应。功能梯度纳米板的特性被认为遵循幂定律横向变化。利用虚拟功原理推导了弹性支撑的功能梯度纳米板的支配振动和屈曲方程，并使用瑞利-里兹方法和特征多项式获得了解。该方法的优点是它消除了有关边缘约束的所有缺点。本文的目的是了解边缘约束，长宽比，材料属性指数，非局部参数，以及在热环境中嵌入的功能梯度纳米板的无量纲频率和屈曲载荷的基础参数。该研究突出表明，对于更高的模式和/或更高的纵横比，非局部效应是显着的，在分析纳米板时需要考虑这一点。此外，可以观察到，帕斯捷尔纳克（Pasternak）基础的作用在无量纲的频率和功能梯度纳米板的屈曲方面很明显。