Nonlinear vibration and chaos of a moving flexible graphene smart electronic web

•A roll-to-roll smart label graphene web as the research object.•The Runge-Kutta method and the Melnikov method are used to obtain the stable working regions.•The moving web is sensitive to the initial conditions.•The moving web changes state with the change of velocity.•Proper friction can reduce the occurrence of chaos and improve the stability. Flexible graphene smart electronics are a kind of electronic device made of silver or other inorganic material and a flexible graphene web substrate. Because of their flexibility and excellent electronic properties, flexible graphene smart electronics have become a research topic of interest. However, during the mass production process, the high-speed transmission of the continuous tension state is susceptible to external disturbances, which seriously restricts the improvement of the flexible graphene smart electronic printing speed. Therefore, studying the dynamic characteristics of moving flexible graphene electronic materials is of great significance for improving their quality and production efficiency. This paper considers a roll-to-roll smart RFID label graphene web as the research object. Based on the energy functional variational theory, the Bubnov-Galerkin method is used to eliminate the residual value of the dynamic Von Karman partial differential equation, and a discrete forced nonlinear vibration control equation for a moving flexible graphene smart electronic web is established. The Melnikov method is used to obtain the Melnikov function of the orbit parameter for the vibration control equation and solve the conditions of the chaos criterion. Using the fourth-order Runge-Kutta method, the nonlinear vibration phase-plane portraits, Poincare maps, time history diagram, and power spectra of the moving flexible graphene smart electronic web are obtained. The effects of the web moving speed, external damping, and initial system conditions on nonlinear dynamic behaviour are calculated, and the stable and unstable working regions of the moving flexible graphene smart electronic web are obtained. This research provides a theoretical basis for the dynamic stability and vibration control of a moving graphene smart electronic web.