Free Vibrations of a Circular Graphene Sheet with Surface Effect & Geometrical Defects

Graphene sheets have gained much popularity and strong potential applications in design of nano-sized structural elements. Because of production process and constrains conditions, circular graphene sheet may be opposed to structural defect. These defects can be inverted to greater holes as amorphous construction when the graphene sheet is working in room temperature. Some of the defects and pin holes on a circular graphene sheet can be considered as multiple eccentric hole on the sheet. Hence, analyzing behavior of circular graphene sheet with multiple holes is important. According to high surface to volume ratio in single layer graphene sheet, surface effect is not negligible, should be considered. Free vibration of an annular graphene sheet, as the basis of any dynamical analysis, is analytically studied. Multipole Trefftz method as well as the translational addition theorem are employed to consider effects of circular defects on behavior of freely vibrating circular graphene sheet. Kirchhoff plate theory is used to solve the problem. Effects of surface effect parameter are investigated on the natural frequencies. These frequencies are derived by minimum singular value decomposition (SVD) method.