The size-dependent free vibration analysis of a rectangular Mindlin microplate coupled with fluid

In this paper, the size-effect and fluid-structure interaction on the vibrational characteristics of a simply supported rectangular microplate is investigated. The influences of rotary inertia and transverse shear deformation which have the remarkable role in the analysis of moderately thick microplates are considered. The first order shear deformation theory along with the modified couple stress theory has been used to perform the free vibrational analysis of the considered problem. The Hamilton's principle is employed to derive the governing differential equations of motion and the corresponding boundary conditions. The fluid is assumed to be incompressible, inviscid and irrotational. The fluid velocity potential is obtained using the boundary and compatibility conditions. Then the Rayleigh-Ritz method has been applied to calculate the natural frequencies of the system. A convergence study is carried out. The obtained results are compared against available data in the published papers and very good agreements have been observed. Finally by referring to the numerical results, the effects of dimensionless thickness, side to thickness ratio, aspect ratio, material length scale parameter and fluid depth ratio on the natural frequencies are discussed in details.