Vibration analysis of bilayered graphene sheets for building materials in thermal environments based on the element-free method

Graphene sheets are widely applied due to their unique and highly valuable properties, such as energy conservation materials in buildings. In this paper, we investigate the vibration behavior of double layer graphene sheets (DLGSs) in thermal environments which helps probe into the mechanism of energy conservation of graphene sheets in building materials. The nonlocal elastic theory and classical plate theory (CLPT) are used to derive the governing equations. The element-free method is employed to analyze the vibration behaviors of DLGSs embedded in an elastic medium. The accuracy of the solutions in this study is demonstrated by comparison with published results in the literature. Furthermore, a number of numerical results are presented to investigate the effects of various parameters (boundary conditions, nonlocal parameter, aspect ratio, side length, elastic foundation parameter, and temperature) on the frequency of DLGSs.