Transverse waves propagating in carbon nanotubes via a higher-order nonlocal beam model

This paper studies the behavior of flexural waves traveling in carbon nanotubes (CNTs) in a free space and embedded in an elastic matrix. An exact higher-order model for analyzing dynamic behavior of nonlocal elastic beams with circular cross-section is proposed, where shear deformation and rotary inertia are both considered without introducing the shear correction factor. Moreover, traction-free condition at the beam surface is met. Using this model, wave dispersion of CNTs is studied and dispersion relation is obtained for single-walled and double-walled CNTs, respectively. Scale-dependent wave speed is given. The effectiveness and validity of the method are confirmed by comparing obtained numerical results with those based on molecular dynamics simulation, the nonlocal Euler–Bernoulli beam theory and nonlocal Timoshenko beam theory with stress gradient and strain gradient. The effects of the scale coefficient, the surrounding elastic medium and van der Waals force on the phase velocity are expounded.