Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading

This paper studies the vibrational characteristics of double-walled carbon nanotubes (DWNTs) with initial stress using a nonlocal Euler-Bernoulli beam model. Both the effect of initial stress and the effect of small length scale are discussed in detail. The effect of van der Waals forces is incorporated in the formulation. The corresponding resonant vibrational characteristics are presented in detail; they are shown to be very different from those predicted by classical elasticity theory when nonlocal effects are significant. The influence of initial stress in carbon nanotubes on their flexural vibration modes is dependent on the tension or compression form of the initial stress. The investigation of the effects of initial stress on transverse wave propagation in carbon nanotubes may be used as a useful reference for the application and the design of nanoelectronic and nanodrive devices, nano-oscillators, and nanosensors, in which carbon nanotubes act as basic elements.