  An analytical method to investigate wave propagation in single- and double-
walled carbon nanotubes under initial compression stress is presented. The
nanotube structures are treated within the multilayer thin shell approximation
with the elastic properties taken to be those of the graphene sheet. The
governing equations are derived based on Flugge equations of motion. Frequency
equations of wave propagation in single and double wall carbon nanotubes are
described through the effects of initial compression stress and van der Waals
force. To show the effects of Initial compression stress on the wave
propagation in nanotubes, the symmetrical mode can be analyzed based on the
present elastic continuum model. It is shown that the wave speed are sensitive
to the compression stress especially for the lower frequencies.
