Study of scale effects on the vibration of graphene sheets with applications to NEMS - Shakouri, Amir (2013)
In this research work, the flexural vibration of graphene sheet nanostructures is modeled and studied from both atomistic and continuum point of view. The results from the two types of modeling are then compared to investigate the scale effects on the vibration of these nanostructures. Also, the effects of different boundary conditions, in-plane prestress loads and environmental stiffness which are usually encountered in NEMS applications are also studied. A new atomistic structural model is developed to study the flexural vibration of graphene sheets based on the REBO potential. This model is shown to be more accurate for studying the flexural vibration of graphene sheets than the existing atomistic structural model based on AMBER potential. The vibration of graphene sheets is studied for different sizes, chiralities and boundary conditions and with consideration for in-plane forces and environmental stiffness. By comparing the results with those from the equivalent classical thin plate model –with mass and stiffness assumed to be distributed evenly– scale effects are observed and it is shown that graphene sheets does not behave like a classical thin plate in vibration at nanoscale. It is particularly found that graphene sheet nanostructures possess lower natural frequencies than what is predicted by the classical thin plate model and are more sensitive to the existence of the in-plane loads and/or the environmental stiffness. To take the scale effect into consideration, a refined continuum thin plate model is developed based on nonlocal and couple stress theories. To perform the free vibration eigensolution, a new Galerkin-based formulation is presented which is able to deal with different boundary conditions – and in particular, the free edges accurately and in a general manner. It was shown that this model can account for the scale effects by introducing two small scale parameters namely, the nonlocal parameter and the Poisson’s ratio – which is shown to be no longer a property but a parameter. The effects of the small scale parameter on the flexural vibration of the newly-developed thin plate model are parametrically studied with consideration for different boundary conditions, in-plane forces and environmental stiffness and it is qualitatively shown that the newly developed nonlocal couple stress thin plate model is able to simulate the scale effects previously observed in the vibrational behavior of graphene sheets.