An order reduction method for single-walled carbon nanotubes with multi-vacancy defects

Presented here is a novel method of reducing the computational cost of analyzing the vibrational properties of a single-walled carbon nanotube (CNT) containing multi-vacancy defects (MVDs), while maintaining a high degree of accuracy. This reduced-order model method is described as modal domain reduction (MDR). In the MDR method, a linearized model of a perturbed CNT is first transformed into modal coordinates derived from the pristine system, taking into account the differences in the numbers of degrees of freedom for the pristine CNT and the CNT with MVDs. Next, the system is divided into primary modes, on the basis of the frequency range of interest, and remaining or secondary modes. The impact of secondary modes on primary modes is captured by the dynamic condensation method. The accuracy of MDR is demonstrated on linearized models of nanotubes of differing diameter and chirality and with different sized MVDs. The natural frequencies and normal modes of these reduced-order models are calculated and compared to the results for the full-order systems.