Analytical and numerical modeling of higher order free vibration characteristics of single-walled carbon nanotubes

In this article, analytical and numerical investigations of small, higher, and asymptotic order vibration eigenmodes and natural eigenfrequencies of single-walled carbon nanotubes (CNT) are elaborated. The nonlocal elasticity theory is used and the numerical simulation is based on the differential quadrature method. Due to numerical instability, the common analytical forms of eigenmodes can be only used for the first 12 modes or so. New mathematical models for higher eigenmodes and associated eigenfrequencies of CNT are developed. The obtained eigenmodes are well conditioned and numerically stable and may be used as modal bases at any required frequency range.