Effects of residual surface stress and surface elasticity on the nonlinear free vibration of nanoscale plates

This paper studies the influence of surface effects (including the residual surface stress and surface elasticity) on the nonlinear free vibrations of nanoscale plates. The motion equations are derived by using the Hamilton's principle and solved numerically. It is found that the influence of surface effects on the normalized period of nanoscale plates becomes increasingly significant when the thickness of the plate decreases. More importantly, the influence of the surface effects on the normalized vibration period reduces if the initial amplitude of the vibration increases. This tendency is more pronounced for the Mindlin plate theory, which includes the transverse shear effect of the plates. In addition, it is found that both the positive residual surface stress and surface elasticity increase the magnitude of the vibration velocity.