The role of the spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates is investigated in this study. The key achievement of this work is that the classical nonlocal elasticity theory is modified to take into account the dependence of nonlocal parameters on the varying of materials through the thickness of the functionally graded sandwich nanoplates. Hamilton’s principle is adopted to establish the governing equations of motion using a new inverse hyperbolic shear deformation theory. Numerical results are carried out via Navier’s solution for the fully simply supported rectangular functionally graded sandwich nanoplates, and they are compared with the available results to confirm the accuracy and efficiency of the proposed algorithm. Besides, the effects of some parameters such as the spatial variation of the nonlocal parameters, the aspect ratio, the side-to-thickness ratio as well as the power-law index on the free vibration of the nanoplates are also investigated cautiously. The results show that the variation of the nonlocal parameters plays a significant role in the free vibration of the functionally graded sandwich nanoplates, which is never investigated in the literature. The present methodology could be applied to the design and application of the micro/nanostructures.

本研究研究了非局部参数的空间变化对功能梯度三明治纳米板自由振动的作用。这项工作的主要成就是对经典的非局部弹性理论进行了修改，以考虑非局部参数对通过功能梯度夹层纳米板厚度的材料变化的依赖性。采用新的反双曲剪切变形理论，采用汉密尔顿原理建立运动控制方程。数值结果是通过 Navier 对完全简支矩形功能梯度夹层纳米板的解决方案进行的，并将它们与可用结果进行比较，以确认所提出算法的准确性和效率。除了，还仔细研究了一些参数，如非局部参数的空间变化、纵横比、侧厚比以及幂律指数对纳米板自由振动的影响。结果表明，非局部参数的变化在功能梯度夹心纳米板的自由振动中起着重要作用，这在文献中从未被研究过。本方法可应用于微/纳米结构的设计和应用。结果表明，非局部参数的变化在功能梯度夹心纳米板的自由振动中起着重要作用，这在文献中从未被研究过。本方法可应用于微/纳米结构的设计和应用。结果表明，非局部参数的变化在功能梯度夹心纳米板的自由振动中起着重要作用，这在文献中从未被研究过。本方法可应用于微/纳米结构的设计和应用。