Free vibrations of thin rectangular nano-plates using wave propagation approach

• Free vibrations of graphene sheet are analyzed based on non-local elasticity.
• Transmission and reflection matrices are found using wave propagation method.
• A new nonlocal parameter is proposed for zigzag and armchair graphene sheets.
• The cut-off frequency is independent of the type of the boundary conditions.
• Increasing nonlocal parameter decreases cut-off frequency.

The wave propagation approach is one of the most powerful techniques used in vibration problems. This method gives the propagation and reflection matrix which is useful for the analysis of mechanical energy transmission in micro/nano devices like energy harvester devices. In this paper, wave propagation approach is used to analyze the free vibrations analysis of thin rectangular macro and nano-plates. Firstly, the propagation and reflection matrices for thin rectangular plates are derived. Then, these matrices are combined to provide a concise and exact approach for obtaining the natural frequencies of the thin rectangular plates. In the macro scale, solution obtained by this approach is exactly the same as those derived by classical method. In Nano-scale, the results are compared with Molecular dynamic simulation of a graphene sheet. Finally, the behavior of reflection coefficients, as an index for energy transmission, under changing the frequency for various nonlocal parameters is studied.