Validity assessment of aspect ratios based on Timoshenko-beam model: Structural design

Emad Ghandourah, Muzamal Hussain, Mohamed A. Khadimallah, Mashhour Alazwari, Mohamed R. Ali and Mohammed A. Hefni

Abstract

In this paper, Timoshenko-beam model is developed for the vibration of double carbon nanotubes. The resulting frequencies are gained for axial wave mode and length-to-diameter ratios. The natural frequency becomes more prominent for lower length-to-diameter ratios and diminished for higher ratios. The converse behavior is observed for axial wave mode with clamped-clamped and clamped-free boundary conditions. The frequencies of clamped-free are lower than that of clampedclamped boundary condition. The eigen solution is obtained to extract the frequencies of double walled carbon nanotubes using Galerkin's method through axial deformation function. Computer softer MATLAB is used for formation of frequency values. The frequency data is compared with available literature and found to be in agreement.

Key Words

axial wave mode; double walled carbon nanotubes; frequency data; Timoshenko-beam model

Address

Emad Ghandourah: Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan Mohamed A. Khadimallah: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia Mashhour Alazwari: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia Mohamed R. Ali: Faculty of Engineering and Technology, Future University in Egypt New Cairo 11835, Egypt; Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha, Egypt Mohammed A. Hefni: Mining Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

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