Vibration analysis of horn-shaped single-walled carbon nanotubes embedded in viscoelastic medium under a longitudinal magnetic field

Based on nonlocal Euler-Bernoulli beam theory, vibration characteristics are investigated for a horn-shaped single-walled carbon nanotube (SWCNT) which is embedded in a viscoelastic medium and subjected to a longitudinal magnetic field. Governing equations of motion are derived for vibration analysis of horn-shaped SWCNTs, where the Lorentz magnetic force, the surrounding viscoelastic medium and variable cross-section have been taken into consideration. Subsequently, perturbation method (PM) and transfer function method (TFM) are employed to compute the natural frequencies and the corresponding mode shapes for horn-shaped SWCNTs with arbitrary boundary conditions. The obtained results are first compared with the results available in the literature, where good agreement is achieved. The validation of the model is followed by a detailed parametric study of the effects of nonlocal parameter, taper parameter and longitudinal magnetic field on the vibration of horn-shaped SWCNTs. The results demonstrate the efficiency of the developed model for vibration analysis of a complicated multi-physics system comprising horn-shaped SWCNTs, viscoelastic medium and a magnetic field in longitudinal direction.