Effects of surface energy on the mechanical performance of nanosized beams

On nanoscales, the influence of surface energy on the mechanical behavior of nanosized structural elements becomes prominent, owing to the increasing ratio of surface area to bulk. However, there are clear discrepancies in previous models on the analysis of residual surface stress. In the present paper, through the principle of minimum potential energy, we formulate the influence of surface energy on the mechanical performance of nanosized beams. The governing equation is similar to that of surface elasticity, but the boundary conditions at free end are distinct from those of the conventional elasticity. As examples, the static deformation and the free vibration of nanosized cantilevers are considered to display the effects of surface energy on nanoscales.