Nonlocal continuous models for forced vibration analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes

•Forced lateral vibrations of 2D and 3D ensembles of SWCNTs are examined.•Novel discrete and continuous models are developed based on nonlocal Rayleigh beam.•The efficiencies of the proposed 2D and 3D contentious models are studied.•A good agreement between the results of discrete and continuous models is reported.•Roles of intertube distance and load frequency on dynamic response are addressed.

Novel nonlocal discrete and continuous models are proposed for dynamic analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes (SWCNTs). The generated extra van der Waals forces between adjacent SWCNTs due to their lateral motions are evaluated via Lennard-Jones potential function. Using a nonlocal Rayleigh beam model, the discrete and continuous models are developed for both two- and three-dimensional ensembles of SWCNTs acted upon by transverse dynamic loads. The capabilities of the proposed continuous models in capturing the vibration behavior of SWCNTs ensembles are then examined through various numerical simulations. A reasonably good agreement between the results of the continuous models and those of the discrete ones is also reported. The effects of the applied load frequency, intertube spaces, and small-scale parameter on the transverse dynamic responses of both two- and three-dimensional ensembles of SWCNTs are explained. The proposed continuous models would be very useful for dynamic analyses of large populated ensembles of SWCNTs whose discrete models suffer from both computational efforts and labor costs.

Graphical abstractNovel nonlocal continuum-based discrete and continuous models are proposed for vibration analysis of two- and three-dimensional arrays of SWCNTs.Figure optionsDownload full-size imageDownload as PowerPoint slide