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A new method for evaluating the natural frequency in radial breathing like mode vibration of double‐walled carbon nanotubes
Author(s) -
FatahiVajari Alireza
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600234
Subject(s) - vibration , natural frequency , van der waals force , carbon nanotube , normal mode , chirality (physics) , concentric , physics , mode (computer interface) , materials science , equations of motion , mechanics , classical mechanics , mathematical analysis , acoustics , mathematics , geometry , nanotechnology , quantum mechanics , computer science , chiral symmetry breaking , quark , molecule , nambu–jona lasinio model , operating system
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.