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The present work investigates the nanoscale vibration behavior of double-layered graphene sheets (DLGSs) resting on elastic medium taking into account effects of van der Waals (vdW) interactions. The analysis is carried out employing meshless method (MLSA) based on the nonlocal elastic plate theory. The DLGSs is modeled by a double thin elastic nanoplates continuum model which account for the small scale effect. The collocation method is adopted to solve the strong form of equilibrium equations and enforcing the boundary conditions. The efficiency of the proposed approach is demonstrated by a comparison with an exact solution computed by the Navier's method. The effects of aspect ratio, stiffness of surrounding elastic medium and nonlocal parameter on the vibration behavior of (DLGSs) are performed.
