Role of Fourier sine transform on the dynamical model of tensioned carbon nanotubes with fractional operator
Kashif Ali Abro, J. F. Gómez‐Aguilar
Abstract
The metallic or semiconducting characteristics of cylindrical graphitic tubes (single‐walled carbon nanotubes) exhibit strongest fibers in the world subject to their chirality and diameter. In this manuscript, the dynamical model of tensioned carbon nanotubes based on Euler–Bernoulli beam subject to single‐walled carbon nanotubes is investigated. The fractional calculus approach has been treated on the dynamical model of tensioned carbon nanotubes through Atangana–Baleanu differentiation. For the sake of proper deflection of single‐walled carbon nanotubes, the thermal expansion coefficient and flexural rigidity are emphasized on deflection of single‐walled carbon nanotubes. The two types of fractional and mathematical solutions have been explored by means of combined implementation of Laplace and Fourier sine transforms. Additionally, the dynamical influence of pretension on the deflection of single‐walled carbon nanotubes has been addressed graphically. Finally, the parametric study of this manuscript has envisaged the utilization of single‐walled carbon nanotubes as per thermo‐physical and structural applications.