Analysis of radial breathing mode of vibration of single-walled carbon nanotubes via doublet mechanics

This paper investigates the radial breathing mode (RBM) vibration of single-walled carbon nanotubes (SWCNTs) based on doublet mechanics (DM) with a length scale parameter. A second order partial differential equation that governs the RBM vibration of SWCNTs is derived. Using DM, the relation between natural frequency and length scale parameter is derived in the RBM mode of vibration. It is shown that the length scale parameter plays significant role in the RBM vibration response of SWCNTs. The length scale parameter decreases the natural frequency of vibration compared to the predictions of the classical continuum models. However, with increase in tube radius, the effect of the scale parameter on the natural frequency decreases. The results obtained herein are compared with the existing theoretical and experimental results and good agreement with the latter is observed. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim