Direct strength measurement of Timoshenko-beam model: Vibration analysis of double walled carbon nanotubes
Emad Ghandourah,Muzamal Hussain,Faisal Al Thobiani,Mohammed Hefni,Sami Alghamdi
Abstract
In the last ten years, many researchers have studied the vibrations of carbon nanotubes using different beam theories. The nano- and micro-scale systems have wavy shape and there is a demand for a powerful tool to mathematically model waviness of those systems. In accordance with the above mentioned lack for the modeling of the waviness of the curved tiny structure, a novel approach is employed by implementing the Timoshenko-beam model. Owing to the small size of the micro beam, these structures are very appropriate for designing small instruments. The vibrations of double walled carbon nanotubes (DWCNTs) are developed using the Timoshenko-beam model in conjunction with the wave propagation approach under support conditions to calculate the fundamental frequencies of DWCNTs. The frequency influence is observed with different parameters. Vibrations of the double walled carbon nanotubes are investigated in order to find their vibrational modes with frequencies. The aspect ratios and half axial wave mode with small length are investigated. It is calculated that these frequencies and ratios are dependent upon the length scale and aspect ratio.
Emad Ghandourah — Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38040, Faisalabad, Pakistan
Faisal Al Thobiani — Marine Engineering Department, Faculty of Maritime Studies, King Abdulaziz University, Jeddah, Saudi Arabia
Mohammed Hefni — Mining Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
Sami Alghamdi — Electrical and Computer Engineering Department, King Abdulaziz University, Jeddah, Saudi Arabia; Center of Nanotechnology, King Abdulaziz University, Jeddah, Saudi Arabia
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