Shakti S. Gupta

Buckling of single-walled carbon nanotubes using two criteria

We use molecular mechanics simulations with the MM3 potential to study instabilities in clamped-clamped single-walled carbon nanotubes (SWCNTs) deformed in torsion and axial compression. The following are the two criteria employed to find the critical buckling strain: (i) a sudden drop in the potential energy and (ii) an eigenvalue of the mass weighted Hessian of the deformed configuration becoming zero. The instability under axial compression is investigated for zigzag and armchair SWCNTs, and that under torsional deformations is also studied for chiral tubes. In general, values of critical strains from the 2nd criterion are found to be substantially less than those from the 1st criterion. For chiral SWCNTs, the critical strains from the 2nd criterion and the potential energies at the onset of instability markedly depend upon the twisting direction. Values of buckling strains predicted from the column and the shell buckling theories are found to agree well with those obtained using the 2nd criterion.

Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

We study the dynamics of an inclined tensioned, heavy cable traveling with a constant speed in the vertical plane. The cable is modeled as a beam resisting bending and shear. The governing equation for the transverse in-plane vibrations of the cable are derived through the Newton-Euler method. The cable dynamics is also studied in the limit of zero bending stiffness. In all cases, application of en- ergy balance reveals that the total energy of the system fluctuates even though the oscillations are small and bounded in time, indicating that the system is nonconser- vative. A comprehensive stability analysis is carried out in the parameter space of inclination, traveling speed, pre-tension, bending rigidity and the slenderness of the cable. Effect of damping is also considered. We conclude that, while pre-tension, rigidity and slenderness enhance the stability of the traveling cable, the angle of inclination affects the stability adversely. These results may act as guidelines for safer design and operation.