Longitudinal, transverse, and torsional vibrations and stabilities of axially moving single-walled carbon nanotubes

• Exploring axial, transverse, and torsional vibrations of axially moving SWCNTs.
• Solving nonlocal governing equations of motion via Galerkin method.
• Specifying the divergence and flutter instability regions for the moving SWCNT.
• Determining roles of small-scale and aspect ratio on the stabilities of the SWCNT.
• Variations of the axial, lateral, and torsional frequencies vs. SWCNT's speed.

Thanks to the brilliant mechanical properties of single-walled carbon nanotubes (SWCNTs), they are suggested as high speed nanoscale vehicles. To date, various aspects of vibrations of SWCNTs have been addressed; however, vibrations and instabilities of moving SWCNTs have not been thoroughly assessed. Herein, vibrational properties of an axially moving SWCNT with simply supported ends are studied using nonlocal Rayleigh beam theory. Employing assumed mode and Galerkin methods, the discrete governing equations pertinent to longitudinal, transverse, and torsional motions of the moving SWCNT are obtained. The resulting eigenvalue equations are then numerically solved. The speeds corresponding to the initiation of the instability within the moving nanostructure are calculated. The roles of the speed of the moving SWCNT, small-scale parameter, and aspect ratio on the characteristics of longitudinal, transverse, and torsional vibrations of axially moving SWCNTs are scrutinized. The obtained results show that the appearance of the small-scale parameter would result in the occurrence of both divergence and flutter instabilities at lower levels of the speed.