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This paper studies the free vibration of size-dependent functionally graded material (FGM) microplates in contact with viscous fluid. The Mori-Tanaka model is applied to formulate the continuous gradual variation of material properties of FGM microplates along thickness direction. A non-classical microplate model is established based on the modified couple stress theory, which considers the size effect by introducing the material length scale parameter. A physical neutral plane is introduced to eliminate the stretching-bending coupling effect. The motion of viscous fluid is defined by Navier-Stokes equations, with which the hydrodynamic loading on microplates is determined with consideration of inertial effect and viscous damping effect. The governing equations for FGM microplates in contact with viscous fluid are derived using the Hamilton's principle and solved by differential quadrature method. Numerical results are obtained to discuss the influences of the aspect ratio, fluid depth, slenderness ratio, fluid viscosity, gradient index, fluid density, and size parameter on the vibration behaviours of microplates in contact with viscous fluid.

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