Large-amplitude vibrations of nanowires with dissipative surface stress effects

In this study, nonlinear free vibrations of doubly clamped Euler–Bernoulli nanowires (NWs) have been considered. The von Kármán strain–displacement relationships along with the classic Zener model are implemented to derive the nonlinear differential equation of the flexural motion of NW. Nonlinear natural frequencies are calculated using the computer package Mathematica. The effects of size-dependent surface dissipation, mode numbers, and amplitude of vibrations on the nonlinear natural frequencies are investigated. It is shown that the surface dissipation effect on the normalized nonlinear natural frequencies depends on the amplitudes of vibrations. Also, comparisons are made with the results published in previous studies.