Decoupling the effects of material thickness and size scale on the transverse free vibration of BNNTs based on beam models

Abstract

Here we establish a new model to decouple the material thickness and elastic property of single-walled boron nitride nanotubes, and thus we can evaluate natural frequencies of transverse free vibration by directly using the Timoshenko beam and Euler-Bernoulli beam models. Full atomic simulations regarding on the vibration behaviors are also presented for comparison. The determination procedure of thickness and the physical meaning of scale parameter for one-atomic thick material are clearly defined. In order to comprehensively unfold the influence of the selection of tubular thickness on natural frequencies, a series of assumed tubular thickness is also adopted to analyze the sources of error and its trend, and finally confirms the accuracy of our proposed result. The accuracy of the beam models is also found to be dependent on the type of boundary constraints. The precision of the beam theory improves for weaker boundary constraints due to the release of shear stresses. The paper heals the rift between atomic simulations and continuum theories.