A New Non local Cylindrical Shell Model for Axisymmetric Wave Propagation in Carbon Nanotubes

In this paper, an analytic nonlocal shell model is established to investigate the axisymmetric wave propagation in carbon nanotubes. Considering carbon nanotubes as continuum elastic shells and applying the nonlocal elasticity theory, the novel governing equations of motion for carbon nanotubes with nanoscale effects are derived based on the variational principle. The dispersion relation of phase velocity in terms of wavenumber for waves to propagate in carbon nanotubes are illustrated and compared with the results predicted by other approaches including the previous partial nonlocal models, classical elastic models, strain gradient theory and molecular dynamic simulation. The analysis and results confirm that this new analytical nonlocal shell model is capable of successfully predicting stiffness enhancement for carbon nanotubes with nonlocal effects and the decay of wave propagation at high wavenumber. Illustration of phase velocity with respect to the nonlocal nanoscale parameter of carbon nanotubes further confirm the rationality of this new, analytical nonlocal shell model in the studies of wave propagation in carbon nanotubes.