effect of geometrical defect on free vibration of a circular graphene sheet using trefftz method

because of production process and constrains conditions, circular graphene sheet may be opposed to structural defect and pin hole, respectively. some of the defects and pin hole on a circular graphene sheet can be considered as an eccentric hole on the sheet. hence, analyzing behavior of circular graphene sheet with an eccentric hole is important. free vibration of an eccentric annular graphene sheet, as the basis of any dynamical analysis, is analytically studied. nonlocal theory of plate is used to solve the problem. trefftz method is used to model the free vibration of graphene with an eccentric hole. effects of nonlocality and eccentricity are investigated on the natural frequencies. these frequencies are derived by singular value decomposition (svd) method.