Circumferential nonlocal effect on vibrating nanotubules

In this paper the nonlocal shell and beam theories are used to study the transverse vibration of slender NTs. The agreement between the shell model and molecular dynamics simulations shows that the nonlocal effect originates predominantly from the atom-atom interaction in circumferential direction. It thus does not decrease with rising axial wavelength. In this case, a nearly constant nonlocal coefficient e0 can be achieved for vibrating NTs. These behaviors however cannot be captured by the widely used nonlocal beam theory where only the axial nonlocal effect is included. Thus, caution must be taken when the one-dimensional nonlocal model is applied to slender NTs.