The role of spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates

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.