Nonlinear oscillations of elliptical and sector prefabricated nanoplate-type structures made of functionally graded building material

Abstract

The primary goal of this work is to apply for the first time the efficient isogeometric type of numerical solving technique for the geometrically nonlinear large-amplitude oscillations of nanoplates with arbitrary shapes with variable thicknesses incorporating simultaneously strain gradient size and nonlocality dependencies. Microplate thickness variation follows convex, concave, and linear patterns. Accordingly, isogeometric analysis is carried out to obtain precise geometrical description and higher-order efficient smoothness related to thickness variation within an arbitrary shape with no difficulty in meshing. It is assumed that nanoplates are made of functionally graded composite materials with variable material properties at different thicknesses. It is found that changing thickness variation pattern from convex to linear, and finally to concave increases the significance of both nonlocality and strain gradient size effects. Moreover, it is demonstrated that by increasing plate deflection and material gradient index, the contributions of strain gradient and nonlocal stress to the nonlinear frequency of functionally graded composite nanoplates are weakened.