Chaotic vibrations of double-layer graphene sheet system.

Nonlinear vibrations of double-layer nanoplate system are studied by numerical simulation. The governing equations are derived on a base of the nonlocal elasticity theory, von Kármán nonlinear theory, and Kirchhoff's hypotheses. Both layers are assumed to be with the same material properties, while interaction between them is taken by the Winkler model. Discretization of the system of governing differential equations is performed by the Bubnov-Galerkin method with the two-mode approximation model, and the obtained system of ordinary differential equations is analysed by the Runge–Kutta method. The study of a linearized system allows the construction of regions of instability. The application of nonlinear dynamics methods made it possible to determine the nature of oscillations when stability is lost, and when small-scale effects are manifested. • Nonlinear vibrations of double-layer graphene system under in-plane load are studied; • the nonlocal governing system based on von Kármán nonlinear relations is applied; • the proposed approach uses the Bubnov-Galerkin method with the two-mode model; • the Floquet theory is used to define instability zones; • it is concluded that small-scale effects on the stability zones are not significant; • small-scale effects can influence the nature of vibrations after loss of stability. [ABSTRACT FROM AUTHOR]