Advances in nano research

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A simplified directly determination of natural frequencies of CNT: Via aspect ratio

  • Banoqitah, Essam Mohammed (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khadimallah, Mohamed A. (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) ;
  • Ghandourah, Emad (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Yahya, Ahmad (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Basha, Muhammad (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Alshoaibi, Adil (Department of Physics, College of Science, King Faisal University)
  • Received : 2021.12.13
  • Accepted : 2022.06.07
  • Published : 2022.09.25
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Abstract

In this paper, a novel model is developed for frequency behavior of single walled carbon nanotubes. The governing equation of motion is constructed method based on the Sander theory using Rayleigh-Ritz's method The frequencies enhances on increasing the power law index using simply supported, clamped and clamped free end conditions. The frequency curve for C-F is less than other conditions. It is due to the physical constraints which are applied on the edge of the CNT. It is observed that the C-F boundary condition have less frequencies from the other two conditions. The frequency phenomena for zigzag are insignificant throughout the aspect ratio. Moreover when index of power law is increased then frequencies increases for all boundary conditions. The natural frequency mechanism for the armchair (10, 10) for various values of power law index with different boundary conditions is investigated. Here frequencies decrease on increases the aspect ratio for all boundary conditions. The frequency curves of SS-SS edge condition is composed between the C-C and C-F conditions. The curves of frequency are less significant from small aspect ratio (L/d = 4.86 ~ 8.47) and decreases fast for greater ratios. It is found that the frequencies via aspect ratios, armchair (10, 10) have higher values from zigzag (10, 0). It is due to the material structure which is made by the carbon nanotubes. The power law index have momentous effect on the vibration of single walled carbon nanotubes. The present frequency result is also compared numerically experimentally with Raman Spectroscopy.

Keywords

Acknowledgement

This research work was funded by Institutional Fund Projects under grant no (IFPHI-031-135-2020).Therefore, authors gratefully acknowledge technical and financial support from the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

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