Effect of small size on wave propagation in double-walled carbon nanotubes under temperature field

The effect of small size on wave propagation in double-walled carbon nanotubes (DWCNTs) under temperature field is investigated using the Euler-Bernoulli beam model. Dynamic governing equations of the carbon nanotube are formulated on the basis of nonlocal thermal elastic theory. The effects of temperature change and van der Waals forces between the inner and outer nanotubes are taken into account. Results show the significance of the small-scale effect on wave propagation in DWCNTs and that some properties of transverse vibrations of DWCNTs are dependent on the change in temperature. The results demonstrate the great potential of the proposed nonlocal beam theory in studying wave propagation in CNTs including thermal effects and also indicate the limitations of local continuum mechanics in analysis of small-scale effects. The work should be useful in the design and application of nanoelectronics and nanoelectromechanical devices.