Advances in nano research

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Vibration of SWCNTs: Consistency and behavior of polynomial law index with Galerkin's model

  • Khadimallah, Mohamed A. (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) ;
  • Hussain, Muzamal (Department of Mathematics, Government College Universit Faisalabad) ;
  • Khedher, Khaled Mohamed (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Bouzgarrou, Souhail Mohamed (Civil Engineering Department, Faculty of Engineering, Jazan University) ;
  • Al Naim, Abdullah F. (Department of Physics, College of Science, King Faisal University) ;
  • Naeem, Muhammad Nawaz (Department of Mathematics, Government College Universit Faisalabad) ;
  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Iqbal, Zafar (Department of Mathematics, University of Sargodha) ;
  • Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University)
  • Received : 2020.04.04
  • Accepted : 2020.09.28
  • Published : 2020.11.25
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Abstract

In this article, vibration attributes of single walled carbon nanotubes based on Galerkin's method have been investigated. The influence of power law index subjected to different end supports has been overtly examined. Application of the Hamilton's variational principal leads to the formation of partial differential equations. The effects of different physical and material parameters on the fundamental frequencies are investigated for armchair and zigzag carbon nanotubes with clamped-clamped, simply supported and clamped-free boundary conditions. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of Single-Walled Carbon Nanotubes (SWCNTs) are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. MATLAB software package has been utilized for extracting tube frequency spectra. The obtained results are confirmed by comparing with available literature.

Keywords

Acknowledgement

The research team thanks the efforts of King Khalid University in financing this applied research and providing all the facilities (laboratories, hardware, and software) in the College of Engineering. In addition, special thanks to Civil Engineering Department where this applied research work achieved. Finally, thanks again to Deanship of Scientific Research in King Khalid University to continue to support scientific research until it becomes among the best universities locally and internationally. Within the framework of small research projects given by the Deanship of Scientific Research the grant number is 123.

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