Timoshenko beam model for buckling and vibration of nanowires with surface effects

In this paper, surface effects on the axial buckling and the transverse vibration of nanowires are examined by using the refined Timoshenko beam theory. The critical compression force of axial buckling and the natural frequency of nanowires are obtained analytically, in which the impacts of surface elasticity, residual surface stress, transverse shear deformation and rotary inertia have been included. The buckling and vibration behaviour of a nanowire is demonstrated to be size dependent, especially when its cross-sectional dimension reduces to nanometres. The surface effects with positive elastic constants tend to increase the critical compression force and the natural frequency, especially for slender nanowires, while the shear deformation lowers these values for stubby nanowires. This study may be helpful to accurately measure the mechanical properties of nanowires and to design nanowire-based devices and systems.