Continuum study on the oscillatory characteristics of carbon nanocones inside single-walled carbon nanotubes

Abstract

This article aims to present a comprehensive study on the oscillatory behavior of concentric carbon nanocones (CNCs) inside carbon nanotubes (CNTs) using a continuum approach. To this end, the optimum radius of nanotube for which the nanocone lies on the tube axis is determined based on the distribution of suction energy. Using the Runge–Kutta numerical integration scheme, the equation of motion is solved numerically to attain the time history of displacement and velocity of nanocone. It is observed that the oscillation of nanocone occurs with respect to its axial equilibrium distance which moves further away from the middle axis of nanotube as the number of pentagons increases. A novel semi-analytical expression as a function of geometrical parameters, initial conditions and cone vertex direction is also proposed for the precise evaluation of oscillation frequency. With respect to the proposed frequency expression, a detailed parametric study is conducted to get an insight into the effects of number of pentagons, cone vertex direction and initial conditions on the oscillatory behavior of CNC–CNT oscillators. It is found that nanocones with more pentagons generate greater maximum frequencies inside nanotubes. Furthermore, it is shown that higher maximum frequencies can be achieved if the nanocone enters the nanotube from base.