Nonlocal surface energy effect on free vibration behavior of nanoplates submerged in incompressible fluid

摘要

This research aims to investigate the free vibration characteristics of a nanoplate sinking in an incompressible fluid, so that the plate is in touch with the fluid from its upper surface. The nonlocal continuum theory together with Gurtin-Murdoch elasticity theory are employed to examine the influence of size-dependency and surface energy effect, respectively. In order to model the fluid-plate interaction, the Navier-Stokes equation is utilized, and the motion equations are solved through implementing Galerkin weighted residual method. The results show that the impact of fluid on shifting the nanoplate natural frequencies to the lower values highly depends on the small-scale parameter. Furthermore, for certain value of the length-to-thickness ratio, while the effects of nonlocal and surface energy parameters are considered to be negligible, the natural frequencies of the submerged nanoplate significantly overestimate the values obtained in the presence of these parameters. This means that, in order to precisely predict the system natural frequencies, it is important to include the impact of size-dependency and surface energy in the mathematical formulation.