Wave propagation analysis in viscoelastic Timoshenko nanobeams under surface and magnetic field effects based on nonlocal strain gradient theory

Abstract

In this work, wave propagation in viscoelastic Timoshenko nanobeam under surface stress and magnetic field effects is studied. The governing equations of the non-local strain gradient theory are reformulated incorporating the Kelvin-Voigt visco-elastic constitutive model under the effect of surface stress and longitudinal magnetic field. The effect of longitudinal magnetic field on the behavior of single walled carbon nanotubes is modeled using the Lorentz magnetic forces. Gurtin-Murdoch’s surface elasticity is used to account for the surface stresses. The closed-form solutions are developed for the reformulated governing equations. The results obtained agree well with the existing literature in the limiting case of no surface and magnetic field effects. It is observed that with the introduction of surface stress values, the damping ratio of both flexural and shear waves increases. The effect of magnetic field, non-locality and strain gradient on phase velocity of flexural and shear waves, threshold and blocking diameters of carbon nanotubes is also presented.