Mathematical Modeling of Nonlinear Vibrations of Single-Walled Carbon Nanotubes

In this article, the nonlinear vibrations of single-walled carbon nanotubes were discussed. The governing equations of each layer are connected with those of its neighboring layers via the Van der Waals interlayer forces. By comparing the new results to those from earlier research, the effects of changes in the geometrical parameters of the nanotubes and the material constants of the elastic media around them on the vibration characteristics are studied. The variational iteration technique (VIM), the Adomian decomposition method (ADM), and the new homotopy perturbation method are compared. These strategies are solid and effective for resolving various linear and nonlinear differential equations that can appear in various branches of research and engineering. Also contrasting with numerical simulations are our results. The answers derived using these three methods and a numerical solution agrees extremely well. Please be aware that your name and affiliation and if applicable those of your co-author(s) will be published as presented in this proof. If you want to make any changes, please correct the details now. Please note that after publication corrections won’t be possible. Due to data protection we standardly publish professional email addresses, but not private ones, even if they have been provided in the manuscript and are visible in this proof. If you or your co-author(s) have a different preference regarding the publication of your mail address(s) please indicate this clearly. If no changes are required for your name(s) and affiliation(s) and if you agree with the handling of email addresses, please respond with “Ok”. The author and co-author names and affiliations are correct.