Abstract
In this paper we extend our previous work to show that there is an effect of initial stress on the dilatation wave propagation in single-wall carbon nanotubes. The nanotube structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The equation of motion of the dilatation wave is obtained using the nonlocal elastic theory. The phase velocity and the group velocity are derived, respectively. The dispersion relation is analyzed with different wave numbers, scale coefficients and initial stress parameter. It can be observed from the results that the dispersion properties of the dilatation wave are induced by small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. In particular, the group velocity of dilatation wave are sensitive to initial compression stress for higher frequencies and insensitive for lower frequencies. The investigation presented may be helpful in the application of CNTs, such as ultrahigh-frequency resonators, electron emission devices, high-frequency oscillators and mechanical sensors.