Bilaterally nonlocal dynamics of layer-by-layer assembly of double-walled carbon nanotubes accounting for intertube rigorous van der Waals forces

Abstract

Based on appropriate nonlocal continuum models, free vibrations of a group of double-walled carbon nanotubes (DWCNTs) with forest configuration are going to be studied carefully. The nanosystem has been embedded in an elastic material such that the exterior nanotubes interact with the adjacent environment. The constitutive tubes of the nanosystem are modeled via nonlocal Rayleigh and high-order beams and all existing van der Waals forces between the walls of different DWCNTs are appropriately included in the developed models. Using the Hamilton's principle, the complex equations of motion of the nanosystem are obtained by exploiting two continuous and discrete models with some effort. For two conditions of the exterior tubes, the frequency analyses are carried out using assumed mode method and Galerkin approach based on discrete and continuous models. A close comparison of the results of the discrete models and those of the continuous ones demonstrates the success of the newly developed continuous models. These models would be very useful in the analysis of populous nanosystems. Finally, the crucial roles of the geometry of the nanotubes, intertube distance, lateral stiffness of the nearby matrix, and the nonlocality on the frequencies are investigated.