The present study focuses on analysing the behaviour of wave propagation in carbon nanotubes along with the characterization of the buckling phenomenon. The carbon nanotubes are modelled as continuum shells that utilize the nonlocal theory of elasticity as these consider the small effects of the nano structures. The expression for the dispersion relation of the wave propagation in single-walled carbon nanotube (SWCNT) and the double-walled carbon nanotubes (DWCNTs) are achieved using a suitable mathematical treatment. For the case of SWCNT, a combined effect of uniform external lateral pressure, uniform axial pressure, stretching of middle surface, the shearing force due to the torque applied, scaling effect are considered, which presents a new concept. The van der Waals (vdW) interaction, additionally, is regarded for the case of DWCNTs. Moreover, the expression for the buckling phenomenon of the DWCNTs and the triple-walled carbon nanotubes (TWCNTS) taking account of the effect of stretching of middle surface, the shearing force due to torque applied, scaling effect, vdW interaction, and net pressure due to vdW interaction has been established. As a special case of the problem, the deduced results of the present study are found to be well-matched with the pre-existing results, hence, validates the undertaken study. The phase velocity and buckling load curves are manifested graphically using numerical data of two distinct kinds of DWCNTs and TWCNTs depending on the armchair configuration. The influence of various affecting parameters the phase velocity and buckling load curves are noted and are illustrated in tabular form. The study may find its potential application for some engineering problems dealing with the characterization of CNTs and wave propagation through them under the combined effect.

本研究的重点是分析碳纳米管中波的传播行为以及屈曲现象的特征。碳纳米管被建模为利用非局部弹性理论的连续壳，因为它们考虑了纳米结构的微小影响。通过适当的数学处理，可以得到单壁碳纳米管（SWCNT）和双壁碳纳米管（DWCNT）中的波传播的色散关系式。对于SWCNT，考虑了均匀的外部横向压力，均匀的轴向压力，中间表面的拉伸，由于施加的扭矩引起的剪切力，结垢效应的综合作用，这提出了一个新的概念。此外，对于DWCNT，还考虑了范德华（vdW）相互作用。而且，DWCNT和三壁碳纳米管（TWCNTS）的屈曲现象的表达式考虑了中间表面的拉伸效应，施加的扭矩引起的剪切力，结垢效应，vdW相互作用以及vdW引起的净压力互动已建立。作为该问题的特例，发现本研究的推论结果与先前的结果非常吻合，因此验证了所进行的研究。使用两种不同类型的DWCNT和TWCNT的数值数据，根据扶手椅的配置，以图形方式显示相速度和屈曲载荷曲线。记录并以表格形式显示了各种影响参数对相速度和屈曲载荷曲线的影响。