Bending and resonance behavior of nanowires based on Timoshenko beam theory with high-order surface stress effects

A high-order surface stress model is incorporated in a continuum mechanics model based on Timoshenko beam theory to investigate the bending and resonance behavior of nanowires (NWs). Closed-form expressions are derived for the deflection curves and the rotation angle for bending of NWs with different boundary conditions. Normalized maximum deflection, effective size-dependent Youngʹs moduli, and resonance frequency of NWs are also presented in analytic forms in terms of the diameter of the NWs and other material parameters. Our results are compared with the experimental data and with previous results based on classical models of Euler–Bernoulli beam theory with simple and refined surface stress model. We find that for NWs with relatively small cross-sectional size the effect of high-order surface stress is significant. While for NWs with relatively large cross-sections the Timoshenko beam model, accounting for the shearing deformation effect, is critical to attain a sufficient accuracy. This suggests that, for a continuum mechanics modeling of NWs valid for a wide range of slenderness ratio, the present continuum mechanics method, utilizing the Timoshenko beam model together with the high-order surface stress effects, could be a feasible tool to analyze the bending and resonance behavior for NWs.