Impacts of surface irregularity on vibration analysis of single-walled carbon nanotubes based on Donnell thin shell theory

Mahmoud M. Selim, Saad Althobaiti, I.S. Yahia, Ibtisam M.O. Mohammed, Amira M. Hussin and Abdel-Baset A. Mohamed

Abstract

The present work is an attempt to study the vibration analysis of the single-walled carbon nanotubes (SWCNTs) under the effect of the surface irregularity using Donnell`s model. The surface irregularity represented by the parabolic form. According to Donnell`s model and three-dimensional elasticity theory, a novel governing equations and its solution are derived and matched with the case of no irregularity effects. To understand the reaction of the nanotube to the irregularity effects in terms of natural frequency, the numerical calculations are done. The results obtained could provide a better representation of the vibration behavior of an irregular single-walled carbon nanotube, where the aspect ratio (L/d) and surface irregularity all have a significant impact on the natural frequency of vibrating SWCNTs. Furthermore, the findings of surface irregularity effects on vibration SWCNT can be utilized to forecast and prevent the phenomena of resonance of single-walled carbon nanotubes.

Key Words

Donnell thin shell theory; irregularity; single-walled carbon nanotubes; vibration analysis

Address

Mahmoud M. Selim: Department of Mathematics, Al-Aflaj College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Al-Aflaj, 11912, KSA/ Department of Mathematics, Suez Faculty of Science, Suez University, Egypt Saad Althobaiti: Department of Sciences and Technology, Ranyah University Collage, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia I.S. Yahia: Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia/ Research Center for Advanced Materials Science (RCAMS), King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia/ Nanoscience Laboratory for Environmental and Biomedical Applications (NLEBA), Semiconductor Lab., Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt Ibtisam M.O. Mohammed: Department of Mathematics, Al_ukhwa College of science and Art, Al-Baha University, Al_mukhwa, Saudi Arabia Amira M. Hussin and Abdel-Baset A. Mohamed: Department of Mathematics, Al-Aflaj College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Al-Aflaj, 11912, KSA

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