Vibration of Black Phosphorus Nanotubes via Orthotropic Cylindrical Shell Model

Black phosphorus nanotubes (BPNTs) may have good properties and potential applications. Determining the vibration property of BPNTs is essential for gaining insight into the mechanical behaviour of BPNTs and designing optimized nanodevices. In this paper, the mechanical behaviour and vibration property of BPNTs are studied via orthotropic cylindrical shell model and molecular dynamics (MD) simulation. The vibration frequencies of two chiral BPNTs are analysed systematically. According to the results of MD calculations, it is revealed that the natural frequencies of two BPNTs with approximately equal sizes are unequal at each order, and that the natural frequencies of armchair BPNTs are higher than those of zigzag BPNTs. In addition, an armchair BPNTs with a stable structure is considered as the object of research, and the vibration frequencies of BPNTs of different sizes are analysed. When comparing the MD results, it is found that both the isotropic cylindrical shell model and orthotropic cylindrical shell model can better predict the thermal vibration of the lower order modes of the longer BPNTs better. However, for the vibration of shorter and thinner BPNTs, the prediction of the orthotropic cylindrical shell model is obviously superior to the isotropic shell model, thereby further proving the validity of the shell model that considers orthotropic for BPNTs.