Vibration analysis of a microplate in contact with a fluid based on the modified couple stress theory

In this study, the hydrostatic vibration analysis of an isotropic rectangular microplate in partial contact with a bounded fluid is studied. Modified couple stress theory based on the Kirchhoff plate assumptions are used to mathematically model the problem. The extended Hamilton’s principle is employed to drive the governing differential equation of motion and the corresponding boundary conditions. The transverse displacement of the microplate is approximated by a set of admissible functions which must satisfy the geometric boundary conditions. The fluid is assumed to be incompressible, inviscid and irrotational and the fluid velocity potential is obtained using the boundary and compatibility conditions. Natural frequencies of the microplate are calculated using the Rayleigh-Ritz method. To validate the present results, the natural frequencies of an isotropic macroplate in contact with fluid are compared with the available data in the literature and very good agreements are observed. Finally using the numerical data, the effect of different parameters such as thickness to length scale parameter, aspect ratio, length to thickness ratio and boundary conditions on the natural frequencies of the microplate are discussed in detail. We have observed that the difference between the natural frequencies predicted using the classical theory and the one evaluated by the modified couple stress theory is significant when thickness of the microplate is small, but diminishes as thickness increases.