Sound wave propagation in single-walled carbon nanotubes with initial axial stress

This paper studies the vibrational characteristics of single-walled carbon nanotubes (SWNTs) with initial axial loading based on the theory of nonlocal elasticity. The consistent equations of motion for the nonlocal Euler-Bernoulli and Timoshenko beam models are provided taking into account the initial axial stress. The small scale effect on CNT wave propagation dispersion relation is explicitly revealed for different CNT wave numbers and diameters by theoretical analyses and numerical simulations. In addition, the applicability of the two beam models is explored by numerical simulations. The research work reveals the significance of the effects of small scale, transverse shear deformation and rotary inertia on wave propagation in short SWCNTs with initial axial loading.