Vibrational Analysis of Zigzag and Armchair Fixed Free Single Walled Boron Nitride Nanotubes: Atomistic Modeling Approach

This paper illustrates the vibrational behavior of single walled boron nitride nanotubes (SWBNNTs) using finite element method (FEM). To this end, atomistic model for both zigzag and armchair chiralities of the single walled boron nitride nanotubes for fixed-free boundary condition is analyzed and their natural frequencies and corresponding mode shapes are obtained. The fixed-free SWBNNTs with different aspect ratios (length/diameter) for both types of chairality are modeled as space frames by considering three dimensional elastic beams and point masses. The elastic properties for beam element are considered based on mechanical characteristics of the BN bond in the hexagonal lattice. The masses of B and N atoms are assumed as point masses at the ends of BN bond. Implementing the finite element simulation approach, the natural frequencies of fixed-free SWBNNTs are computed. Results pertaining to bending, torsional and axial modes of vibration are reported with discussions. The present approach is found to be time saving and different chiralities can be easily incorporated in terms of real atomic structures. The results shows, that as the size of fixed free SWBNNTs in terms of length as well as diameter increases the natural frequencies of free vibration decreases, and the zigzag form of fixed-free SWBNNTs are more sensitive compare to armchair form.