Resonant frequency analysis of Timoshenko nanowires with surface stress for different boundary conditions

Abstract

The influence of both surface and shear effects on the resonant frequency of nanowires (NWs) was studied by incorporating the Young-Laplace equation with the Timoshenko beam theory. Face-centered-cubic metal NWs were studied. A dimensional analysis of the resonant frequencies for fixed-fixed gold (100) NWs were compared to molecular dynamic simulations. Silver NWs with diameters from 10 nm–500 nm were modeled as a cantilever, simply supported and fixed-fixed system for aspect ratios from 2.5–20 to identify the shear, surface, and size effects on the resonant frequencies. The shear effect was found to have a larger significance than surface effects when the aspect ratios were small (i.e., <5) regardless of size for the diameters modeled. Finally, as the aspect ratio grows, the surface effect becomes significant for the smaller diameter NWs.