Bending, buckling and vibration of size-dependent functionally graded annular microplates

Abstract

The bending, buckling and free vibration of annular microplates made of functionally graded materials (FGMs) are investigated in this paper based on the modified couple stress theory and Mindlin plate theory. This microplate model incorporates the material length scale parameter that can capture the size effect in FGMs. The material properties of the FGM microplates are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique. The higher-order governing equations and boundary conditions are derived by using Hamilton’s principle. The differential quadrature (DQ) method is employed to discretize the governing equations and to determine the deflection, critical buckling load and natural frequencies of FGM microplates. A parametric study is then conducted to investigate the influences of the length scale parameter, gradient index and inner-to-outer radius ratio on the bending, buckling and vibration characteristics of FGM microplates with hinged–hinged and clamped–clamped supports. The results show that the size effect on the bending, buckling and vibration characteristics is significant when the ratio of the microplate thickness to the material length scale parameter is smaller than 10.