A Study On Vibrations of Nanorod using Timoshenko Beam Theory Under the Influence of Magnetic Field

Abstract

The transverse vibrations of a thin graphene rod under the influence of a magnetic field are investigated. An analytical method is developed to solve the frequencies of the transversely vibrating graphene rod. Explicit results are obtained using Timoshenko beam theory as a function of wavenumber and phase velocity and numerical results are performed. It is observed that when the difference in magnetic field strength is minor, the influence of beam slenderness on frequencies becomes magnified. Finally, it is found that the hardness or softening impact of the beam model can be controlled by varying the field strength.