Transverse wave propagation in viscoelastic single-walled carbon nanotubes with surface effect based on nonlocal second-order strain gradient elasticity theory

Abstract

Nowadays, the viscoelastic carbon nanotubes (CNTs) have been used as one of the most promising candidates for nanodevices (or nanoelectronics) and super-strong reinforcement fibers in polymer nanocomposites. In recent years there have been many papers that considered the effects of material length scales in the investigations of the material constants related on the structural parameters on the wave propagation in the viscoelastic CNTs. By using different approaches, for examples, Eringen’s differential nonlocal model, modified couple stress theory, and strain gradient theories, the stiffness softening or strengthening effect can be well predicted. However, the influence of the rapid stiffness enhancing effect on the wave characteristics of the viscoelastic CNTs is still not reported. To deal with such problem, this work aims to investigate the transverse wave propagation in viscoelastic single-walled carbon nanotubes (SWCNTs) adhered by surface material based on the nonlocal second-order strain gradient elasticity theory. The characteristic equation of wave motion of the viscoelastic SWCNTs with surface effect is systematically formulated to achieve the analytical dispersion relation between the wave frequency (or phase velocity) and the wave number. In the end, some most important conclusions are concluded.