Dynamic interactions of doubly orthogonal stocky single-walled carbon nanotubes

Nonlocal continuum-based modeling of free transverse vibration of doubly orthogonal stocky single-walled carbon nanotubes (DOSWCNTs) which are embedded in an elastic matrix is of particular interest. A basic step towards such a crucial goal is to establish a rational model for evaluating the van der Waals interactional force between two tubes. By employing Hamilton's principle, the nonlocal governing equations associated with the free vibration of the nanosystem are obtained using Timoshenko and higher-order beam theories. Inherently, these are sets of four coupled integro-partial differential equations which are very difficult to be solved analytically. To bridge such a dilemma, reproducing kernel particle method is exploited and the essential boundary conditions of each shear-deformable beam model are exactly satisfied by implementing the corrected collocation method. In a special case, the predicted natural frequencies by the proposed models are checked with those of other models analyzed via mode summation method, and a reasonably good agreement is achieved. Subsequently, the effects of the slenderness ratio, small-scale parameter, aspect ratio, nanotubes' radii, intertube distance, transverse and rotational stiffness of the surrounding elastic medium on free vibration of the nanosystem are comprehensively addressed for various boundary conditions.