Free and forced transverse vibration of nanowires with surface effects

Abstract

This paper presents a theoretical analysis of free vibration and forced vibration of nanowires with surface effects. Using the Timoshenko beam theory incorporated with the surface effects, exact frequency equations are derived for various end supports. Natural frequencies and mode shapes are determined for simply supported, clamped-clamped, and clamped-free ends. Forced vibration of nanowires is also treated by superposing vibration modes of free vibration. An inverse problem is further investigated to determine the size-dependent effective Young's modulus of nanowires. Obtained results for a nanowire with residual stress and surface elasticity are confirmed by comparing them with the results using the finite element method. Theoretical natural frequencies and finite element method simulation have good agreement with the results from experimental data and molecular dynamics simulation. The effect of surface stress on forced vibration is analyzed. Residual surface tension has a more significant influence on the frequencies and a somewhat effect on the mode shapes.