On size-dependent dynamic behavior of rotating functionally graded Kirchhoff microplates

A size-dependent model for free vibration and transient response of rotating functionally graded (FG) microplates is established on the basis of the Kirchhoff plate theory and modified couple stress theory. A microplate made of a two-constituent material with a continuous through-thickness power-law variation is considered. The governing equations of motion as well as boundary conditions containing the von Karman geometric nonlinearity, Coriolis effect and centrifugal stiffening effect are derived by using Hamilton's principle. An assumed-mode discretization approach is applied to solve these equations numerically. The convergence and comparison studies are presented to prove the effectiveness of the current model. Numerical examples are presented for investigating the effects of the size-dependency, non-dimensional angular velocity, FG index and aspect ratio on dynamic properties of rotating FG microplates. It is revealed that the increase of non-dimensional material length scale parameter increases the stiffness of the plate, which accordingly, results in an increase in natural frequencies and a decline of transient responses. The FG index and angular velocity noticeably affect the size dependency of rotating FG microplates.