Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field

•Vibration and instability of a SWCNT under a 3D magnetic field are studied.•The governing equations are constructed based on the nonlocal Rayleigh beam theory.•The frequencies and phase velocities are derived analytically in some special cases.•The explicit expression of the critical transverse magnetic field is obtained.•The role of small-scale and magnetic fields on dynamical characteristics is studied.

The vibration and instability of a single-walled carbon nanotube (SWCNT) under a general magnetic field are of particular interest to researchers. Using nonlocal Rayleigh beam theory and Maxwell’s equations, the dimensionless governing equations pertinent to the free vibration of a SWCNT due to a general magnetic field were derived. The effects of the longitudinal and transverse magnetic fields on the longitudinal and flexural frequencies as well as their corresponding phase velocities were addressed and are discussed below. The critical transverse magnetic field (CTMF) associated with the lateral buckling of the SWCNT was obtained. The obtained results reveal that the CTMF increases with the longitudinally induced magnetic field. Further, its value decreases as the effect of the small-scale parameter increases.

Graphical abstractUsing nonlocal Rayleigh beam model, vibration and instability of a SWCNT subjected to a three-dimensional magnetic field are examined. The transverse magnetic field corresponding to the buckling of the SWCNT is also determined.Figure optionsDownload full-size imageDownload as PowerPoint slide