The vibration model and quality factor analysis of Timoshenko nanowires with surface stress

The Young-Laplace equation was incorporated into Timoshenko beam theory to model the free vibration of bending nanowires while taking into account the surface properties. Three boundary conditions were considered: cantilever, simply-supported and fixed-fixed ends. A method based on Fourier series expansion is introduced to solve for the free vibration solution with specific initial conditions. The quality factor for vibrating nanowires in a viscous environment is calculated based on damping ratio of beams and the influence of surface stress on the quality-factor of bending nanowire sensors is discussed.