On the Modeling of Eigenmodes and Eigenfrequencies of Carbon Graphene Sheets under the Influence of Vacancy Defects

The vibrational behavior of defected graphene sheets was investigated via finite element analysis. The simulations were carried out for perfect and imperfect nano-sheets. This study was conducted to examine the influence of vacant sites on these nano-structures. In the current study, a graphene sheet is considered as a space frame. The natural frequency and corresponding mode shapes of the perfect and defective nano-sheets were obtained and compared. Results are presented as diagrams stating the natural frequency of graphene sheets with respect to the amount of vacancy defects. The results indicate that the natural frequency of nano-sheets reduced by introducing atomic defects to the configuration of these nano-materials. Such impurities lower the vibrational stability of graphene sheets.