Axisymmetric nonlinear free vibration of size-dependent functionally graded annular microplates

In this paper, a non-classical microplate model is developed for the axisymmetric nonlinear free vibration analysis of annular microplates made of functionally graded materials (FGMs) based on the modified couple stress theory, Mindlin plate theory and von Kármán geometric nonlinearity. This non-classical model is capable of incorporating the microplate model with the length scale parameter, geometric nonlinearity, transverse shear deformation and rotary inertia. By using Hamilton's principle, the higher-order governing equations and boundary conditions for the problem are derived. The differential quadrature (DQ) method is employed to discretise the governing equations, which are then solved by a modified iterative method to obtain the nonlinear frequencies of FGM microplates with different boundary conditions. Numerical results are then presented in both tabular and graphical form to investigate the effects of the length scale parameter, gradient index, inner-to-outer radius ratio and radius-to-thickness ratio on the nonlinear free vibration characteristics of FGM microplates. It is found that unlike homogeneous microplates, the FGM microplates display different vibration behavior at positive and negative amplitudes due to the presence of bending-extension coupling.