A study on large amplitude vibration of multilayered graphene sheets

In the present article, large amplitude vibration analysis of multilayered graphene sheets is presented and the effect of small length scale is investigated. Using the Hamilton’s principle, the coupled nonlinear partial differential equations of motion are obtained based on the von Karman geometrical model and Eringen theory of nonlocal continuum. The solutions of free nonlinear vibration, based on the harmonic balance method, are found for graphene sheets with three different boundary conditions. For numerical results single, double and triple layered graphene sheets with both armchair and zigzag geometries are considered. The results obtained herein are compared with those available in the literature for linear vibration of multilayered graphene sheets and an excellent agreement is seen. Also, the effects of number of layers, geometric properties and small scale parameter on nonlinear behavior of graphene sheet are discussed in details.

Research highlights
► In the present article, large amplitude vibration analysis of multilayered graphene sheets is presented and the effect of small length scale is investigated.
► The solutions of free nonlinear vibration, based on the harmonic balance method, are found for graphene sheets with three different boundary conditions.
► The effects of nonlocal parameter, number of layer and aspect ratio on the nonlinear vibration behaviour of multilayered zigzag and armchair graphene sheets are discussed in details.