Vibrational characterization of wavy atomic structures of single walled boron nitride nanotubes

Abstract

This paper illustrates the variation in the natural frequencies of different modes of vibration considering the different types of waviness of the atomic structures of single walled boron nitride nanotubes (SWBNNTs), i.e., sinusoidal, elliptical and parabolic. The waviness present in the atomic structures of SWBNNTs causes a variation in the localized stiffness in waviness regions, thereby affecting the natural frequency of the SWBNNTs. Thus, it is important to understand the effects of the different types of possible waviness present in the atomic structures of SWBNNTs on their natural frequency. A vibrational analysis was performed for the bridged configuration (with both ends fixed) of SWBNNTs. Continuum modelling based analytical and finite element method (FEM) simulation approaches were used to estimate the natural frequencies of SWBNNTs with different types of wavy curvatures. The FEM approach reflects the shear deformation on the natural frequency of wavy nanotubes, whereas inclusion of shear deformation in the analytical approach adds complexity to the model, which requires more computational time for analysis. The obtained results indicate that the sinusoidal curvature of wavy atomic structures of SWBNNTs is more sensitive compared to the parabolic and elliptical curvatures of wavy nanotubes. Mode shape analysis is also found to be useful for estimating the type of curvature in the atomic structures of the nanotube. As presented herein, understanding the effect of waviness on the variation in the natural frequency of the wavy atomic structure of SWBNNTs is found to be useful for the practical realization of wavy atomic structure based nano-mechanical resonators for applications such as in sensor systems on the nano-scale level.