Service ability design of vibrating chiral SWCNTs: Validation and parametric study

Muzamal Hussain , Mohamed R. Ali , Abdelhakim Benslimane , Humaira Sharif , Mohamed A. Khadimallah , Muhammad Nawaz Naeem , Imene Harbaoui , Sofiene Helaili , Aqib Majeed , Abdelouahed Tounsi

Abstract

This paper provides the free vibrations of chiral carbon nanotubes. The governing equations of Flügge theory is considered for vibration frequencies of chiral single walled carbon nanotubes. The solution of frequency equation is obtained from a novel model for better representation of stubby and short vibration characteristics of chiral tubes with clamped-clamped and clamped-simply supported end conditions. For the harmonic response of this tube, the model displacement function is adopted. The variational approach Rayleigh-Ritz method with kinetic and strain energies are used. The Lagragian function is differentiated with respect to unknown functions. The frequency equation is written in compact form to solve with MATLAB software. The frequencies of chiral SWCNTs for first ten aspect ratios as small level are investigated. The results shown as for decreasing the aspect rations, the frequencies are increases. The presented results of this model are verified with experimental and numerical results, which found as an excellent agreement.

Key Words

boundary conditions; chiral SWCNTs; Flügge shell theory; length-to-diameter ratios; Rayleigh-Ritz method

Address

Muzamal Hussain, Humaira Sharif and Muhammad Nawaz Naeem — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Mohamed R. Ali — (1) Faculty of Engineering and Technology, Future University in Egypt New Cairo 11835, Egypt, (2) Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha, Egypt
Abdelhakim Benslimane — Laboratoire de Mécanique Matériaux et Énergétique (L2ME), Département Génie Mécanique, Faculté de Technologie, Université de Bejaia, 06000 Bejaia, Algérie
Mohamed A. Khadimallah — Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia
Imene Harbaoui — Department of Chemical Engineering, College of Engineering, King Khalid University, Abha 61411, Kingdom of Saudi Arabia
Sofiene Helaili — (1) Carthage University, Tunisia Polytechnic School, LASMAP (LR03ES06), La Marsa, Tunisia, (2) Carthage University, ISTEUB, Tunis, Tunisia
Aqib Majeed — Department of Mathematics, The University of Faisalabad, Sargodha Road, University Town Faisalabad, 38000, Pakistan
Abdelouahed Tounsi — (1) YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea, (2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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