Closed form interaction for safety assessment of DWCNTs: Mechanical vibration

Muzamal Hussain , Mohamed A. Khadimallah , Hamdi Ayed , Emad Ghandourah , Abir Mouldi , Abdelouahed Tounsi

Abstract

Here, vibration of double walled carbon nanotubes is evaluated using Euler-Bernoulli beam model. These tubes are placed on Winkler elastic foundation. A simple Galerkin's approach is presented to solve the tube governing equations and for extracting of vibration eigen-frequencies of double walled carbon nanotubes. The procedure is easy for computer programming with various combinations of boundary conditions. The frequency influence is observed with different parameters. Effects of Winkler foundation versus frequencies with varying lengths is examined for a number of boundary conditions. It is noticed that the frequencies are lower for higher length on increasing the Winkler foundation. The frequencies of clamped-clamped are higher than that of clamped simply supported end condition. The obtained results are compared with some experimental ones.

Key Words

boundary conditions; computer programming; double walled carbon nanotubes; Winkler elastic foundation

Address

Muzamal Hussain — Department of Mathematics, University of Sahiwal, Sahiwal, 57000, Pakistan
Mohamed A. Khadimallah — Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia
Hamdi Ayed — Department of Civil Engineering, College of Engineering, King Khalid University, Abha - 61421, Saudi Arabia
Emad Ghandourah — Department of Nuclear Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
Abir Mouldi — Department of Industrial Engineering, College of Engineering, King Khalid University, Abha - 61421, Saudi Arabia
Abdelouahed Tounsi — YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea/ Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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