Axial vibration of single-walled carbon nanotubes using doublet mechanics

This paper investigates the axial vibration of single-walled carbon nanotubes based on doublet mechanics with a length scale parameter. A forth-order partial differential equation that governs the axial vibration mode of single-walled carbon nanotubes is derived. Using doublet mechanics, the relation between natural frequency and length scale parameter is derived in the axial mode of vibration. It is shown that length scale parameter plays significant roles in the axial vibration behavior of single-walled carbon nanotubes. Such effect decreases the natural frequency compared to the predictions of the classical continuum mechanics models. However, with increasing tube length, the scale effect on the natural frequency decreases.