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Vibration analysis of biaxially compressed double-layered graphene sheets based on nonlocal strain gradient theory

ABSTRACT This paper develops a nonlocal strain gradient plate model for vibration analysis of double-layered graphene sheets under biaxial in-plane mechanical loads. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. In fact, frequency increment due to the strain gradient effect is neglected in all previous papers related to double-layer graphene sheets. Governing equations of a nonlocal strain gradient double-layer graphene sheet on elastic substrate are derived via Hamilton's principle. Galerkin's method is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as in-plane loading, nonlocal parameter, length scale parameter, elastic foundation, interlayer stiffness and boundary conditions on vibration characteristics a double-layer graphene sheet are examined.