Symmetries and Conservation Laws of Equations of Motion of Double-Wall Carbon Nanotubes Conveying Fluid

摘要

The paper is concerned with the dynamic behaviour of double-wall carbon nanotubes conveying fluid. The equations of motion of such a "nanopipe" used for the purpose are based on the classical linear model of Bernoulli-Euler elastic beams, several extra terms being added to take into account the impact of the conveyed fluid as well as the van der Waals interaction forces between inner and outer nanotubes and nanotubes - solid plane. We formulate the problem in an exact variational statement and investigate the Lie symmetries of both the governing equations and the associated functional. We derive the conservation laws corresponding to the admitted variational and divergent symmetries by virtue of Bessel-Hagen's extension of Noether's theorem.