Longitudinal Vibrational Analysis of Restrained Irregular Single-Walled Carbon Nanotube Using Thin Cylindrical Shell Model

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Abstract
The main purpose of this work is to investigate the impacts of surface irregularity on the natural frequency of longitudinal vibration of the single-walled carbon nanotube (ISWCNT). The boundary conditions and governing equations are formulated based on thin cylindrical shell theory. An exact solution is presented and the MATLAB R2013a Software is used to carried out the numerical solutions. A novel equation of motion and frequency equation are derived. The impact of various parameters, including surface irregularity, stiffness and thickness, on longitudinal vibration of SWCNT is examined. It is concluded that, the longitudinal natural frequencies of SWCNT increase from large to small irregularity parameter. Additionally, it has been found that increasing the ration (h/R) of nanotube is preferable for improving the vibration stability of SWCNTs. Moreover, the findings of this work can be used to produce the best designs for nanodevices with SWCNT as a common structural component.

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