Dynamic analysis of finite periodic nanoplate structures with various boundaries

• Dynamic response of periodic nanoplate is studied by nonlocal Mindlin plate theory.
• Vibrations of graphene sheets can be greatly reduced by periodic array design.
• Boundary constraint conditions have significant influences on the first band gap.
• High order band gap of periodic nanoplate is slightly affected by boundary condition.

Dynamic responses of the finite periodic nanoplate structures with various boundary conditions are researched by using the wave method. The dynamics model of the nanoplate structure is established based on the nonlocal Mindlin plate theory. From the Fourier transform, the vibration responses of the single layer graphene sheets under various boundary conditions are obtained by the wave method. The dynamic responses of the finite periodic nanoplate can be determined by the continuous and boundary conditions. In the numerical calculation, the natural frequencies of single layer graphene sheets computed by the presented method agree well with those of molecular dynamics (MD) simulation, which verifies the reliability of the present method. It can be found that the dynamic responses of the finite periodic nanoplates are much smaller than those of the uniform nanoplates in some frequencies which are called the band gap frequencies. It is significant to design the periodic array structure for the vibration suppression of the nanoplates. Moreover, the influences of the nanoplate width and thickness and boundary conditions on the dynamic response of the finite periodic nanoplate structures are also studied.