Vibration analysis of rectangular nanoplate immersed in viscous fluid based on modified couple stress theory

This work examines the hydrostatic dynamics of a rectangular nanoplate in contact with a confined fluid. This problem was mathematically modeled using modified couple stress (MCS) theory and classical plate assumptions. The motion differential equation and the boundary conditions have been derived via Hamilton's principle. A velocity potential function is also derived using boundary conditions and compatibility conditions for an incompressible, nonviscous, and nonrotating fluid. A Rayleigh–Ritz technique is then utilized to determine the natural frequencies of nanoplates. It was found that the results of the frequencies of the microplate in contact with the fluid were very similar to those of the previous research and that there was a good agreement between the two. The effect of different factors such as the thickness-to-scale parameter ratio, the length-to-thickness ratio, the length-to-width ratio, and the boundary conditions on natural frequencies has been examined using the obtained results. It has been observed that for a plate with a low thickness, the difference between the natural frequencies expected by the classical as well as MCS theories is large, but this difference disappears as the plate thickness increases.