Effect of stacking order on the vibration properties of bilayer black phosphorus

The effect of the stacking order of bilayer black phosphorus (BLBP) on the vibration properties is investigated by using molecular dynamics (MD) simulation and continuum modelling. The results show that the interlayer shear effect plays a very important role in the vibration behaviours of BLBPs. In MD simulation, a negative shear modulus is found in BLBP nanoresonators with stacking orders AA and AA ', which can decrease the natural frequency of the nanoresonators. The prediction of the natural frequency of the BLBP from the orthotropic sandwich plate model (OSPM) agrees with the MD simulation results very well. Moreover, for the vibration of the high-order mode, the interlayer shear modulus of the OSPM along one direction can mainly influence the natural frequency of the vibration mode, with the antinodes strictly aligning the direction for the BLBP. The results are thus important for understanding the dynamic behaviour of multilayer orthotropic nanostructures and designing multilayer orthotropic nanostructure resonators.