This study provides the axisymmetric static and free vibration analysis of moderately thick functionally graded annular nano-plates with different boundary conditions. The displacement components are assumed based on the Mindlin plate approximation. Further, to reflect the small-scale effects, stress-driven nonlocal elasticity is employed. The bending analysis of nano-plates under uniformly distributed loads and natural frequencies of the plate are obtained by implementing a finite element method. The effect of small scales on transversal displacements and the frequencies of the plate is investigated for different parameters, such as material properties, plate aspect ratios, and different boundary conditions. Finally, the nonlocal stress-driven theory based on the Mindlin and Kirchhoff assumptions is compared. It is observed that the Mindlin model demonstrates more capability in detecting the nonlocal effects when the characteristic parameter takes small values.

本研究提供了具有不同边界条件的中等厚度的功能梯度环形纳米板的轴对称静态和自由振动分析。位移分量是根据 Mindlin 板近似假设的。此外，为了反映小规模效应，采用了应力驱动的非局部弹性。通过有限元方法获得了均匀分布载荷下纳米板的弯曲分析和板的固有频率。针对不同的参数，例如材料特性、板的长宽比和不同的边界条件，研究了小尺度对板的横向位移和频率的影响。最后，对基于Mindlin和Kirchhoff假设的非局部应力驱动理论进行了比较。可以看出，当特征参数取较小值时，Mindlin 模型表现出更强的检测非局部效应的能力。