The dispersion characteristics of the waves propagating in a spinning single-walled carbon nanotube

As the nano-motor becomes a mechanical reality, its prototype can be envisaged as nano-sized rotating machinery at a situation, albeit for different purposes, like that in the first half of the 20th century during which rotor dynamics has contributed to boosting machine power capacity. Accordingly, we take the benefit of hindsight to develop a classical framework of vibration analysis. Essentially, the equations of motion are formulated to cope with both the special carbon-nanotube properties and the first author's previously developed spinning beam formalism, establishing a model satisfactorily verified by some available molecular dynamics (MD) data and classical spinning beam results extracted from the literature. The model is inexpensive based on continuum mechanics as an alternative to the less-flexible MD method for simulating wave motion of the spinning single-walled carbon nanotube, yielding several interesting phenomena, including the fall-off and splitting of the wave characteristic curves and the unexpected gyroscopic phase property. Potential applications are proposed.