Transverse wave propagation in elastically confined single-walled carbon nanotubes subjected to longitudinal magnetic fields using nonlocal elasticity models

Lateral wave propagation in an elastically confined single-walled carbon nanotube (SWCNT) experiences a longitudinal magnetic field is examined using nonlocal Rayleigh, Timoshenko, and higher-order beam theories. The SWCNT is modeled via an equivalent continuum structure (ECS) and its interaction with the surrounding elastic medium is simulated via lateral and rotational continuous springs along its length. For the proposed models, the dimensionless governing equations describing transverse vibration of the SWCNT are constructed. Assuming harmonic solutions for the propagated sound waves, the dispersion equation associated with each model is obtained. Subsequently, the explicit expressions of the frequencies as well as the corresponding phase and group velocities, called characteristics of the waves, are derived for the proposed models. The influences of the slenderness ratio, the mean radius of the ECS, the small-scale parameter, the longitudinal magnetic field, the lateral and rotational stiffness of the surrounding matrix on the characteristics of flexural and shear waves are explored and discussed.