Nonlocal magneto-thermo-vibro-elastic analysis of vertically aligned arrays of single-walled carbon nanotubes

This study concerns with transverse vibrations of magnetically-thermally affected vertically aligned arrays of single-walled carbon nanotubes (SWCNTs) using nonlocal elasticity theory of Eringen. Using nonlocal Rayleigh and Timoshenko beam theories, both discrete and continuous versions of equations of motion are presented. In contrast to the discrete models, the continuous models do not suffer from huge time and labor costs for nanosystems with high population. The capability and efficiency of the continuous models in capturing the frequencies of the discrete models are displayed, and a reasonably good agreement is obtained. Subsequently, the influences of radius of SWCNTs, slenderness ratio, population, small-scale parameter, strength of magnetic field, and variation of the temperature on the fundamental frequency are explained and discussed. Additionally, the role of shear deformation on the obtained results is explained and the limitations of the nonlocal Rayleigh beam model are revealed.