Nonlocal vibrations and potential instability of monolayers from double-walled carbon nanotubes subjected to temperature gradients

Using nonlocal elasticity theory of Eringen, free transverse thereto-elastic vibrations of vertically aligned double walled carbon nanotubes (DWCNTs) with a membrane configuration is going to be explored methodically. Accounting for nonlocal heat conduction along the side walls of DWCNTs with allowance of heat dissipation from the outer surfaces, the nonlocal temperature fields within the constitutive tubes are assessed for a steady-state regime. The van der Waals interactional forces between atoms of each pair of DWCNTs as well as the innermost and outermost tubes are displayed by laterally continuous springs whose constants are appropriately evaluated. By establishing suitable discrete and continuous models on the basis of the Rayleigh and higher-order beam theories, nonlocal in-plane and out-of-plane vibrations of thermally affected nanosystems of monolayers of DWCNTs are examined and discussed. The critical values of the temperature change are stated explicitly and the role of influential factors on this crucial factor as well as the free vibration behavior are investigated in some detail. Through conducting a fairly comprehensive numerical study, the influences of the slenderness ratio, temperature change in the low and high temperatures, number of nanotubes, small-scale parameter, intertube distance, and stiffness of the surrounding environment on the nonlocal-fundamental frequency are explained. The obtained results from this work could provide crucial guidelines for the design of membranes or even jungles of vertically aligned DWCNTs as thermal interface nanostructures.