Influence of Thermal and Magnetic Field on Vibration of Double Walled Carbon Nanotubes Using Nonlocal Timoshenko Beam Theory

In this paper, the influence of thermal and magnetic field on transverse vibration of double walled carbon nanotubes are investigated using nonlocal Timoshenko beam theory. The governing equation of motion with small scale effects are formulated by considering thermal and Lorentz magnetic force. The dispersion relation is derived for carbon nanotubes with simply supported ends and the numerical simulations are done using MATLAB. Dispersion curves are drawn for both double and single walled carbon nanotubes for different mode and magnetic field strength. The numerical result shows that the strength of magnetic field increases the natural frequencies and the nonlocal parameter decreases the natural frequencies of carbon nanotubes. Further to discuss the accuracy of the present result, the dispersion curves of single walled carbon nanotubes obtained by omitting the magnetic field are compared with the existing literature.