Thermal effect on wave propagation behavior of viscoelastic carbon nanotubes conveying fluid with the spinning and longitudinal motions

Abstract

In this paper, the thermal effect on wave dispersion characteristic induced by the spinning and longitudinal motions in the viscoelastic carbon nanotubes (CNTs) conveying fluid is presented. Hamilton’s principle is utilized to derive the governing equation of this nanotube based on the non-local strain gradient and Euler–Bernoulli beam theories. Then, the dispersion solution is found by using the Naiver method. Based on this, the influences of the spinning and longitudinal motion velocities, structural damping, temperature and flow velocity on dispersion relation of the nanotubes are discussed according to numerical simulation. In view of the results of numerical examples, some interesting conclusions can be drawn. The existence of spinning motion leads to the coupling between the vibration in the [Formula: see text] and [Formula: see text] directions, which induces that the first-order transverse wave frequency increases/decreases for small/large wave number and the second-order one increases. The important solutions presented in the work will provide the useful information for the designation of the nanotubes conveying fluid with the spinning and longitudinal motion.