size-dependent free vibration analysis of rectangular nanoplates with the consideration of surface effects using finite difference method

in this article, finite difference method (fdm) is used to study the size-dependent free vibration characteristics of rectangular nanoplates considering the surface stress effects. to include the surface effects in the equations, gurtin-murdoch continuum elasticity approach has been employed. the effects of surface properties including the surface elasticity, surface residual stress and surface mass density are considered to be the main causes for size-dependent behaviors that arise from the increase in surface-to-volume ratios at smaller scales. numerical results are presented to demonstrate the difference between the natural frequency obtained by considering the surface effects and that obtained without considering surface properties. it is observed that the effects of surface properties tend to diminish in thicker nanoplates, and vice versa.