Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory

This paper develops a Mindlin microplate model based on the modified couple stress theory for the free vibration analysis of microplates. This non-classical plate model contains an internal material length scale parameter related to the material microstructures and is capable of interpreting the size effect that the classical Mindlin plate model is unable to describe. The higher-order governing equations of motion and boundary conditions are derived using the Hamilton principle. The p-version Ritz method is employed to determine the natural frequencies of the microplate with different boundary conditions. A detailed parametric study is conducted to study the influences of the length scale parameter, side-to-thickness ratio and aspect ratio on the free vibration characteristics of the microplate. It is found that the size effect is significant when the thickness of microplate is close to the material length scale parameter.