Vibration analysis of double-walled carbon nanotubes based on Timoshenko beam theory and wave propagation approach

Emad Ghandourah, Muzamal Hussain, Amien Khadimallah, Abdulsalam Alhawsawi, Essam Mohammed Banoqitah and Mohamed R. Ali

Abstract

This paper concerned with the vibration of double walled carbon nanotubes (CNTs) as continuum model based on Timoshenko-beam theory. The vibration solution obtained from Timoshenko-beam theory provides a better presentation of vibration structure of carbon nanotubes. The natural frequencies of double-walled CNTs against half axial wave mode are investigated. The frequency decreases on decreasing the half axial wave mode. The shape of frequency arcs is different for various lengths. It is observed that model has produced lowest results for C-F and highest for C-C. A large parametric study is performed to see the effect of half axial wave mode on frequencies of CNTs. This numerically vibration solution delivers a benchmark results for other techniques. The comparison of present model is exhibited with previous studies and good agreement is found.

Key Words

beams theory; continuum model; micro/nano tubes; natural frequencies; vibrational modes; vibration structure

Address

Emad Ghandourah, Abdulsalam Alhawsawi and Essam Mohammed Banoqitah: Department of Nuclear Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia/ Center for Training & Radiation Prevention, King Abdulaziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38040, Faisalabad, Pakistan Amien Khadimallah: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulazi University, Al-Kharj, 11942, 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, Egypt

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