A Shell Model for Free Vibration Analysis of Carbon Nanoscroll

Abstract

Carbon nanoscroll (CNS) is a graphene sheet rolled into a spiral structure with great potential for different applications in nanotechnology. In this paper, an equivalent open shell model is presented to study the vibration behavior of a CNS with arbitrary boundary conditions. The equivalent parameters used for modeling the carbon nanotubes are implemented to simulate the CNS. The interactions between the layers of CNS due to van der Waals forces are included in the model. The uniformly distributed translational and torsional springs along the boundaries are considered to achieve a unified solution for different boundary conditions. To study the vibration characteristics of CNS, total energy including strain energy, kinetic energy, and van der Waals energy are minimized using the Rayleigh-Ritz technique. The first-order shear deformation theory has been utilized to model the shell. Chebyshev polynomials of first kind are used to obtain the eigenvalue matrices. The natural frequencies and corresponding mode shapes of CNS in different boundary conditions are evaluated. The effect of electric field in axial direction on the natural frequencies and mode shapes of CNS is investigated. The results indicate that, as the electric field increases, the natural frequencies decrease.

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“…Meanwhile, the Chebyshev surrogate model–based interval uncertain methodology was used for structure and vehicle suspension optimization. () Recently, the free vibration analysis of a carbon nanoscroll shell model was investigated by Taraghi et al in which the Chebyshev polynomial was used to evaluate the natural frequencies and the corresponding mode shapes of carbon nanoscroll in different boundary conditions. However, with the increase of the number of interval variables, the high‐order ICPE method with many sample data has to be used to achieve a satisfied accuracy.…”