A nonlocal shell theory model for evaluation of thermoelastic damping in the vibration of a double-walled carbon nanotube

Thermoelastic damping (TED) is a major factor of dissipating energy in the vibration control of nanodevices. On the other hand, application of classic theory in the study of nanostructures is not reasonable. In this paper, a model based on nonlocal shell theory, accounting for the small-scale effects, is used to investigate thermoelastic vibration behavior and damping of double-walled carbon nanotubes (DWCNTs) with simply supported boundary conditions. The inner and outer carbon nanotubes are considered as two individual thin shells. The set of general thermoelastic coupled equations are numerically solved. The results show that the small-scale effects decrease natural frequencies and increase thermoelastic damping compared to the local model, especially for the coaxial frequency and large circumferential wave numbers. The numerical results also show that when the radius of nanotubes rises, the influence of small-size effect on natural frequencies and thermoelastic damping drops dramatically.