Nonlocal free vibration characteristics of power-law and sigmoid functionally graded nanoplates considering variable nonlocal parameter

Abstract

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.