Viscoelastic wave propagation in the viscoelastic single walled carbon nanotubes based on nonlocal strain gradient theory

• The characteristic equation for viscoelastic wave in embedded viscoelastic SWCNTs is derived.
• The critical propagation condition for viscoelastic wave is obtained.
• A blocking diameter is observed, above which the wave could not propagate in SWCNTs.
• Larger nonlocal parameter/smaller material length scale parameter decrease blocking diameter.

In this paper, the viscoelastic wave propagation in an embedded viscoelastic single-walled carbon nanotube (SWCNT) is studied based on the nonlocal strain gradient theory. The characteristic equation for the viscoelastic wave in SWCNTs is derived. The emphasis is placed on the influence of the tube diameter on the viscoelastic wave dispersion. A blocking diameter is observed, above which the wave could not propagate in SWCNTs. The results show that the blocking diameter is greatly dependent on the damping coefficient, the nonlocal and the strain gradient length scale parameters, as well as the Winkler modulus of the surrounding elastic medium. These findings may provide a prospective application of SWCNTs in nanodevices and nanocomposites.