Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

Abstract

Carbon nanotubes fascinate new materials with astonishing mechanical, optical, and electrical properties. In fact, carbon nanotubes are kinds of rolled graphene sheets, and the rolling manner shows the basic properties of the tube, and that is actually the main reason for the extraordinary feature of the carbon nanotubes. This paper aims to presents formulation of Love’s shell theory for single-wall carbon nanotubes (SWCNTs) using Galerkin’s method. For this system, the governing equation is developed with proposed method. It is assumed that C–C and C–F support conditions are applied on the edge of carbon nanotube. Zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different mode and in-plane rigidity with end conditions. Moreover, the influence of mass density per unit lateral area on the same structure is also developed. It is also concluded that the fundamental frequencies of chiral tubes are lower than that of zigzag tubes frequencies. By increasing values of in-plane rigidity, resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. Though the trends of frequency values of both mass density per unit lateral area and in-plane rigidity are converse to each other. It is shown that variation in mass density has a significant effect on the vibration of SWCNTs. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used. Tube dynamical equations for the present problem are taken in the integral form energy expressions for a carbon nanotube. The axial modal deformations are approximated by making use of the beam functions. The proposed model is continuum-model for getting the dynamic character of SWCNTs and to validate the results by earlier methods.