Non-local effect on the vibration analysis of double walled carbon nanotubes based on Donnell shell theory

Abstract

Abstract This piece of work describes a free vibration analysis of double walled carbon nanotubes (DWCNTs) based on non-local elastic shell model. The classical Donnell's shell theory is engrossed to account the effects of small scale by merging Eringen's non-local elasticity equations into it. The wave propagation approach is implemented to analyse the influence of various edge conditions and also van der Waals interaction forces between inner and outer tubes given due consideration. An eigen value problem is formed to investigate the frequency spectra of DWCNTs in relevance of aspect ratio and distinct values of non-local parameter. The results in current study show the ability to perform free frequency characteristics of DWCNTs by developed non-local elastic shell model with appropriate choice of material properties has been certified by experimental comparisons with molecular dynamic data and also verified by earlier computations.