Effects of initial axial stress on waves propagating in carbon nanotubes using a generalized nonlocal model

This paper studies the dispersion relation of waves propagating in 1D nanostructures with initial axial stress. Based on a nonlocal elastic model incorporating with strain gradient, the governing equations for longitudinal and transverse waves in bars and beams have been derived, respectively. In this equation, two scale parameters are introduced to describe size effect. The phase and group velocities of wave propagation are obtained analytically, and the effects of initial axial loading on the wave speeds are analyzed. Examples are presented for flexural waves propagating in single-walled and double-walled carbon nanotubes. Waves are always present for tensile initial axial force, while they may not exist unless the compressive axial force fulfills a certain condition. In particular, the wave speeds are sensitive to initial force for lower frequencies and insensitive to it for higher frequencies.