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

Mohamed A. Khadimallah , Muzamal Hussain , Khaled Mohamed Khedher , Souhail Mohamed Bouzgarrou , Abdullah F. Al Naim , Muhammad Nawaz Naeem , Muhammad Taj , Zafar Iqbal , Abdelouahed Tounsi

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.

Key Words

frequency spectra; volume fraction; polynomial law; clamped support

Address

(1) Mohamed A. Khadimallah — Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, BP 655, Al-Kharj, 11942, Saudi Arabia
(2) Mohamed A. Khadimallah — Laboratory of Systems and Applied Mechanics, Polytechnic School of Tunisia, University of Carthage, Tunis, Tunisia
(3) Muzamal Hussain, Muhammad Nawaz Naeem — Department of Mathematics, Government College Universit Faisalabad, Punjab, Pakistan
(4) Khaled Mohamed Khedher — Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
(5) Khaled Mohamed Khedher — Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia
(6) Souhail Mohamed Bouzgarrou — Civil Engineering Department, Faculty of Engineering, Jazan University, Kingdom of Saudi Arabia
(7) Abdullah F. Al Naim — Department of Physics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
(8) Muhammad Taj — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
(9) Zafar Iqbal — Department of Mathematics, University of Sargodha, Sargodha, Punjab, Pakistan
(10) Zafar Iqbal — Department of Mathematics, University of Mianwali, Punjab, Pakistan
(11) Abdelouahed Tounsi — YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea
(12) Abdelouahed Tounsi — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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