Vibrations of van der Waals heterostructures: A study by molecular dynamics and continuum mechanics

The vibration behaviors of van der Waals (vdW) heterostructures are studied based on molecular dynamics (MD) simulations and continuum mechanics modelling in this paper. Graphene/hexagonal boron nitride and graphene/silicene systems are considered as two typical examples of heterostructures studied here. Our MD results show that the resonance frequency of vdW heterostructures grows as their layer number increases and tends to be saturated when the layer number is relatively large. These findings deviate from results of the conventional composite beam (CB) model of vdW heterostructures. By abandoning the assumptions in the CB model, we propose a novel multiple beam (MB) model giving a result that agrees well with MD results. We find from the MB model that compared to other factors the interlayer shearing effect plays the key role in determining the resonance behaviors of vdW heterostructures. Considering this fact, we further simplify the MB model to a much simpler form which gives a simple but precise description of the vibration behaviors of vdW heterostructures. This simplified MB model suggests that the resonance frequency of vdW heterostructures can be optimized by changing their total mass, the sum of bending stiffness of their component layers, and the sum of interlayer shear modulus of their vdW layers.