Free vibration analysis of nano-plate in viscous fluid medium using nonlocal elasticity

In the present study, the dynamics of the interaction between a Kirchhoff nanoplate and the surrounding fluid is investigated. Using non-local elasticity theory, the influence of small-scale parameter is considered in the governing equation of motion. The Navier-Stokes equations are utilized to model the fluid-solid interaction. The vibration behavior of nanoplate submerged in different viscous fluids with various aspect ratios are simulated in order to analyze the effects of fluid viscosity and density on the free vibration natural frequencies of the nanoplate. The results reveal that, for smaller size parameter, the fluid existence has a remarkable decreasing effect on the nanoplate natural frequencies. Moreover, it has been shown that the fundamental frequency ratio between two cases, first, when the nanoplate is assumed to be under viscous fluid interaction, and second, while the structure vibrates in vacuum environment, remains almost constant with the changes in small-scale parameter.