The effect of fluid surface waves on free vibration of functionally graded microplates in interaction with bounded fluid

In this paper, the modified couple stress theory (MCST) is applied to study the effect of fluid surface waves on free vibration of a functionally graded (FG) microplate in interaction with bounded fluid. The bounded fluid is considered inviscid, irrotational, and incompressible. The fluid velocity potential which satisfies the boundary and compatibility conditions is applied to model the effect of bounded fluid. Assuming that the gradient of material properties varies through the thickness, the classical plate theory has been employed to obtain the frequency equations of the FG microplate; these equations are solved by Rayleigh-Ritz method to determine the natural frequencies. The frequencies are extracted for FG plates, homogeneous microplates, and FG microplates in vacuum and in interaction with bounded fluid. Where the microplate has been in interaction with bounded fluid, influences of microplate bulging and fluid sloshing are captured both simultaneously and separately. Effects of plate dimensions, fluid tank, fluid type, power law index, and length scale parameter on natural frequencies of the system are presented and discussed in details for various boundary conditions. Results show that fluid surface waves significantly affect the natural frequencies of high flexible microplates.