Modified timoshenko beam models for flexural wave dispersion in carbon nanotubes with shear deformation considered

In this paper, the governing equations of modified Timoshenko beam models with stress and strain gradients are established to investigate the nonlocal shear effect on flexural wave dispersion in carbon nanotubes. The dispersion equations are analytically obtained and the dispersion curves of the two modified models are illustrated numerically with different nonlocal shear factors. The results and their analysis show preliminarily that: (1) the nonlocal factors introduced here have significant effects on analyzing the dispersion characteristic of flexural wave in carbon nanotubes, especially at the higher wave numbers; (2) the variations of nonlocal factors also influence the branches of waves depending on the different nonlocal shear factors adopted.