Vibration analysis of circular single layer graphene sheet under temperature changes in thermal environment

Considering broad applications of sheets, specially circular sheets in the industry and the widespread use of nanotechnology to pass from limitations of each branches of science, particularly mechanics of materials and also importance of vibration (or buckling) due to temperature changes or thermal loads, in this thesis, development of relative relations of circular single layer nanographene sheets’ vibrations due to temperature changes, were studied. Nonlocal thin plate theory of Eringen is employed to investigate effects of thermal environment on the behavior of circular single-layer graphene sheet freely vibration containing a circular perforation of arbitrary size and location. In order to analytically solve the equation of motion, the separation of variables method in conjunction with the translational addition theorem for Bessel functions is used. The results of changing various geometric and physical parameters and different kinds of restrains and boundary conditions on the natural frequency of a single layer circular graphene sheet were examined and discussed. In some cases, thermal buckling phenomenon was observed.