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

• Published in: International journal of mechanical sciences 2016-11, Vol.118, p.219-230
• Main Authors: Zhang, D.P., Lei, Y., Shen, Z.B.
• Format: Article
• Language: English
• Subjects: Cross sections; Horn-shaped carbon nanotubes; Magnetic field; Magnetic fields; Mathematical models; Nonlocal continuum theory; Parameters; Single wall carbon nanotubes; Vibration; Vibration analysis; Vibration characteristics; Viscoelastic medium; Viscoelasticity
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2016.09.025

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. •Viscoelastic medium, longitudinal magnetic field and viscoelasticity of horn-shaped SWCNTs are considered simultaneously.•Natural frequencies for the horn-shaped SWCNTs with arbitrary boundary conditions are derived via TFM and PM.•The effect of taper parameter on the natural frequencies decreases significantly with rising nonlocal parameter or the strength of magnetic field.•The influence of magnetic field on the damped frequencies increases with increasing taper or nonlocal parameters.