A new method for evaluating the natural frequency in radial breathing like mode vibration of double-walled carbon nanotubes

This paper investigates the radial breathing like mode (RBLM) vibration of double-walled carbon nanotubes (DWCNTs) based on a new theory called doublet mechanics (DM) with a scale parameter. To this end, DWCNTs are considered as two concentric elastic thin cylindrical shells bounded together with van der Waals (vdW) forces between them. The vdW forces are modeled using Len-Jones potential. Using DM, two coupled second order partial differential equations that govern the RBLM vibration of DWCNTs are derived. Subsequently, the equations of motion are solved to obtain the natural frequencies in the RBLM vibration. It is the first time that DM is used to derive the natural frequencies of the RBLM vibration for DWCNTs. The advantage of these analytical formulas is that unlike the other methods, they are explicitly dependent to scale parameter and chirality effect. It is shown that the chirality and scale parameter play significant role in the RBLM vibration response of DWCNTs. To validate the accuracy and efficiency of this work, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim