Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory

Wave propagation in viscoelastic single walled carbon nanotubes is investigated by accounting for the simultaneous effects of the nonlocal constant and the material length scale parameter. To this end, thin shell theory is used to model the viscoelastic single walled carbon nanotubes, and the nonlocal strain gradient theory is used to account for the effects of the nonlocal constant and the material length scale parameter. The Kelvin-Voigt model is used to model the viscoelastic property, and the governing equations are derived through Hamilton's principle. The viscoelastic single walled carbon nanotube medium is modeled as visco-Pasternak. The results demonstrate that viscoelastic single walled carbon nanotube rigidity is higher in the strain gradient theory and lower in the nonlocal theory in comparison to that in the classical theory. Also, the size effects, nanotube radius, circumferential wavenumber, nanotube damping coefficient, and foundation damping coefficient exert considerable effects on viscoelastic single walled carbon nanotube phase velocity.