Abstract
In the present article, nonlinear free and forced vibration of a bilayer graphene embedded in a polymer medium is studied based on the nonlocal elasticity theory. As a nonlinear function of deflection of graphene sheets, a refined pressure expression is established to describe the van der Waals (vdW) interactions between graphene layers and polymer medium. Assuming the large displacements and anisotropic model for graphene layers, the nonlinear couple partial differential equations of a double layered graphene sheet (DLGS) are obtained. The in-phase and out of phase nonlinear to linear natural frequencies are shown for both zigzag and armchair geometries. The effects of small scale parameter, nonlinear coefficients of vdW between two layers, nonlinear factor of polymer matrix and geometric properties on the nonlinear vibrational behavior of a DLGS are discussed in detail. It is found that the nonlinear vdW coefficient has a significant effect on the out of phase frequencies while the nonlinear polymer coefficient has considerable influence on in-phase frequencies.
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