Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory

Abstract Parametric vibrations of the single-layered graphene sheet (SLGS) are studied in presented work. The equations motion govern geometrically nonlinear oscillations. appearance small effects is analysed due to application nonlocal elasticity theory. approach developed for rectangular simply supported small-scale plate and it employs Bubnov–Galerkin method with a double mode model, which reduces problem investigation system second-order ordinary differential (ODEs). dynamic behaviour micro/nanoplate varying excitation parameter determine chaotic regimes. As well influence change nature studied. bifurcation diagrams, phase plots, Poincaré sections largest Lyapunov exponent constructed analysed. It established that use analysis sheets leads significant alteration character oscillations, including attractors.