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.

在这里，我们建立了一个新的模型来解耦单壁氮化硼纳米管的材料厚度和弹性特性，因此我们可以直接使用 Timoshenko 梁和 Euler-Bernoulli 梁模型来评估横向自由振动的固有频率。还提供了关于振动行为的完整原子模拟以进行比较。明确了单原子厚材料的厚度确定程序和尺度参数的物理意义。为了全面展开管壁厚度选择对固有频率的影响，还采用了一系列假设的管壁厚度来分析误差来源及其趋势，最终证实了我们提出的结果的准确性。还发现梁模型的准确性取决于边界约束的类型。由于剪切应力的释放，梁理论的精度提高了较弱的边界约束。这篇论文弥合了原子模拟和连续理论之间的裂痕。