Vibration Properties of Single Walled Carbon Nanotubes-A Comparison Between the Atomistic Simulations and Continuum Shell Modelling

Free vibration analysis of single-walled carbon nanotubes (SWCNTs) is carried out to study the natural frequencies and mode shapes. Appropriate continuum parameters are proposed for equivalent continuum modelling of SWCNTs. Atomistic simulations and continuum shell modelling are employed for the purpose. The formulation of the stiffness matrix computation of the atomistic model is brought out using a finite difference method to bypass the usage of Young's modulus and wall thickness of SWCNTs. The importance of using equilibrium configuration is highlighted. The large scattered values of Young's modulus and wall thickness of SWCNTs are reported based on the prior atomistic models. The appropriate set of continuum parameters are proposed based on the free vibration analysis of continuum shell model of SWCNTs. The computed natural frequencies and mode shapes given by the continuum shell model are close to that of atomistic computations, provided the wall thickness values (between 0.06 nm to 0.09 nnn) and corresponding Young's modulus of SWCNTs are chosen appropriately.